What is Substitution: Definition and 815 Discussions

A substitution reaction (also known as single displacement reaction or single substitution reaction) is a chemical reaction during which one functional group in a chemical compound is replaced by another functional group. Substitution reactions are of prime importance in organic chemistry. Substitution reactions in organic chemistry are classified either as electrophilic or nucleophilic depending upon the reagent involved, whether a reactive intermediate involved in the reaction is a carbocation, a carbanion or a free radical, and whether the substrate is aliphatic or aromatic. Detailed understanding of a reaction type helps to predict the product outcome in a reaction. It also is helpful for optimizing a reaction with regard to variables such as temperature and choice of solvent.
A good example of a substitution reaction is halogenation. When chlorine gas (Cl2) is irradiated, some of the molecules are split into two chlorine radicals (Cl•) whose free electrons are strongly nucleophilic. One of them breaks a C–H covalent bond in CH4 and grabs the hydrogen atom to form the electrically neutral HCl. The other radical reforms a covalent bond with the CH3• to form CH3Cl (methyl chloride).

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  1. N

    Aromatic Substitution Polarity

    I have just been trying to teach myself about the effect of activating and deactivating groups on electrophilic substitution. However, I am a bit confused as to why the amine group in procaine (anesthetic) is in the para position, when the aromatic ring is attached to a deactivating ester. What...
  2. K

    Mathematica Mathematica: got problem with substitution

    Dear all, I have a problem with my code using the substitution. The code works perfectly without substitution however it does not work with substitution. I mean, I got the results of sub[1], sub[2] and sub[3]. But using the code replacement, I got sub[1] = sub[2] = sub[3], which are not...
  3. S

    Trigonometric / Mixed Integral Involving Substitution

    Homework Statement integrate xarctanx/(x^2 + 1)^2 Homework Equations Integration by parts possibly? I was attempting to do it without integration by parts because we went over this in tutorial and my TA couldn't solve it properly, hence why I'm here. The Attempt at a Solution I...
  4. D

    Integration, U substitution help

    Homework Statement Hi I am having a few problems with the below u substitution can anyone help, In particular what to do with the integral of the u substitution? Homework Equations \int2x2 square root of 1-x3 dx, u = 1-x3 Any pointers would be appreciated Thanks D
  5. N

    Euler substitution (Good sources)

    Anyone know any good sources to read about Euler substitutions from? Both online and books would be suffice. Also videos, if there are any. All help would be greatly appreciated =)
  6. 1

    Is It Necessary to Substitute u in Integrals?

    I received no credit, resulting in an 84 for a few integral problems. I had correct final answers for everything. When I confronted my professor about this, he said it was because I didn't actually put "u" and "du" into the integral. Is that really always necessary? Why actually put the u in...
  7. E

    How are equations used to derive the final solution in this image?

    In the attached image, how are equations 1, 2, 3 and 4 used to come to the final equation of 5 and 6? I am suspecting it has something to do with the derivative with respect to t, but I don't know how they remove it to get the final solution. Am I missing something incredibly simple that is not...
  8. Rasalhague

    Substitution of variables in improper integrals

    What principles apply when making a substitution of variables in an improper integral. I gather that a substitution of variables can change an impoper integral to a proper integral. Can substitution also change a proper integral into an improper integral? Suppose I know that a pair of integrals...
  9. A

    Solve second order diff eq with substitution

    Homework Statement Solve: xy''+2y'=12x^{2} with u=y' Homework Equations if you have: y'+P(x)y=Q(x) then your integrating factor is: I(x)=e^{\int P(x) dx} The Attempt at a Solution The only reason I was able to solve this is because I stumbled upon a...
  10. Q

    Limits and Direct Substitution

    Why wouldn't answer choice "C" be true as well? [PLAIN]http://i.min.us/idPNiK.png Homework Equations I thought that you could use direct substitution on this limit. The Attempt at a Solution I did get answer choices A and B. For the limit to exist, both the left and right hand limits...
  11. A

    Solve Seperable diff eq with substitution

    Homework Statement Solve the differential equation: x \frac {dy}{dx} = y + e^{\frac {y}{x}} with the change of variable: v = \frac {y}{x} Homework Equations The Attempt at a Solution I would just like to know if I have successfully solved the problem. Thanks...
  12. D

    Substitution Rule for Integrals: Solving for the Unknown Variable

    Hello! My problem is the following: Is \int_a^b f(z) dt = \int_{g(a)}^{g(b)} f(z) \frac{1}{g} dz ? \frac{dz}{dt} = g Thank you!
  13. S

    Proof - Substitution, Jacobian, etc.

    Hello! I recently tried to prove following theorem: Let \phi:B\to\mathbb{R}^2 be a diffeomorphism (regular, injective mapping). Then \int_{\phi(B)}f(\mathbf{x})\,\mathrm{d}x=\int_{B}f(\phi(\mathbf{t}))\left|{\mathrm{det}}\mathbf{J}_{\phi}\right|\mathrm{d}t With following I can't proof...
  14. S

    Using substitution to combine integrals

    Homework Statement I want to combine the 2 integrals: \int_{a}^{b}(x-3)f(x)dx+\int_{-b}^{-a}(x-3)f(x)dx Homework Equations given: f(x) is an even function The Attempt at a Solution swap the limits in the second integral: \int_{a}^{b}(x-3)f(x)dx-\int_{-a}^{-b}(x-3)f(x)dx...
  15. S

    Substitution Methods for first order differential equations

    I have the following equation:: xy' = y + 2*sqrt(xy) I know I should either use the F(y/x) substitute or Bernoulli's method of substitution but I'm not sure how to manipulate the equation to determine which it is. If someone had some helpful tips on how to start, please let me know...
  16. W

    Applying Integration by Parts & Trig Substitution

    Homework Statement \int\sqrt{4+9x^{2}}dx Homework Equations Pythagorean Identities? The Attempt at a Solution I find it sort of cumbersome to use the special formatting here, so I hope it is okay that I just photocopied my work on paper. You can see how far I made it, but...
  17. R

    Inverse Hyperbolic Funcs. or Trigonometric Substitution?

    So, in integrals that lead to inverse hyperbolics and can be solved with trigonometric substitution i just get lost. I know how to use both of them but i don't know which to use. For the sake of simplicity i'll just go with this one ∫ dx/sqrt(4+x^2) We know this equals arcsinh(x/2)...
  18. B

    When integrating by trig substitution why do you use what you use?

    when integrating by trig substitution why do you use what you use?? for example int. (1+x^2)^0.5 dx why do you use x= tan u i mean obviously because it works, but if you didn't know it works how would you figure it out? i would think that you should use x=sinh u but I've been trying...
  19. R

    Integration substitution.

    Use substitution to find each indefinite integral. ∫ (square root 2 + lnx) / x ; dx I did u=2+ln(x) then differentiate both sides to get du=0+dx/x ∫ (square root 2 + lnx) / x ; dx ∫ (square root u) du ∫ u^0.5 du u^(3/2)/(3/2)+c =(2+ln(x))^(3/2) +c Is the answer right? Thanks.
  20. P

    Is the Substitution Rule Applicable to Complex Numbers?

    I was reading J. J. Koliha's book on analysis and came across this Do you agree?
  21. T

    Why should I use a substitution here?

    Homework Statement Area = \frac{2}{\sqrt{3}}\int\sqrt{1-\frac{x^{2}}{4e^{2}}}dx Apparently I should use a substitution x/2e = sin(u) and I can see why it's those value but I don't understand why they need the substitution in the first place. Isn't the integral simply...
  22. G

    Simple function substitution question

    Homework Statement if I had a function such that B(p, y) = py - c(y) and then knowing that y=y(p), does that mean B(p) = p^2 - c(p)? Homework Equations The Attempt at a Solution
  23. W

    Solve Substitution Problem: x^2+2y^2=9, x-y+3=0 with x=(-1,-3) and y=(2,0)

    x^2+2y^2=9 x-y+3=0 I have x=(-1,-3) y=(2,0) I don't want to have to write out the whole problem I just want to know if this is correct Can someone tell me if this is correct?
  24. J

    ODE Substitution: Solving Bessel Equation with x=cosθ

    Apparently this is a Bessel equation \sin \theta \frac{d^2 y}{d\theta^2} + \cos \theta \frac{dy}{d\theta} + n(n+1)\sin \theta y = 0 after using x = cos\theta. The problem says use x = cos \theta anyway. A further substitution may be required, but is not alluded to. The variable 'x' is used in...
  25. W

    Solving x^2 + 2y = 9 w/ Sub Method

    use the subtitution method to solve. x^2 + 2y = 9 x - y + 3 = 0 y=x+3 -> (3) substitute for y with x+3, you get: x^2+2(x+3)=9 x2+2x−3=0 factorize it to get: (x+3)(x−1)=0 x=−3,x=1 substitute for each value of x in equation 3 x=−3y=−3+3=0 x=1y=1+3=4...
  26. P

    Integration substitution rule help

    Homework Statement ∫ x^(1/4) . (x^(5/4) +1)^6 Homework Equations I used substitution rule with u = x^(5/4) +1 The Attempt at a Solution I got an answer of 4/5 . (u^7/7) +c would that be correct
  27. H

    Integral with trig substitution

    Homework Statement Using trig substitution integrate x2/(x4+6x2+9) Homework Equations The Attempt at a Solution I'm almost completely positive I need to use partial fraction decomposition... doing this I end up having the integral of 1/(x2+3)-3/(x2+3)2 There aren't any square...
  28. J

    Problem with substitution in a difference equation

    Homework Statement Verify that the response of the system governed by the 1st order different equation y(k)=bu(k)+ay(k-1) is given by this solution y(k)=\frac{b}{1+a}\left [ (-1)^{k}+a^{k+1} \right ] for u(k) = (-1)^k The Attempt at a Solution The solution said we can verify this...
  29. H

    Integration using trig substitution

    Homework Statement Integrate (9x2-16)1/2/x4 Homework Equations The Attempt at a Solution I set 3x=4secy, 3dx=4secytany and (9x2-16)1/2=2tany. I then plugged that all into my integral and ended up with2tany*4secytany/(4/3secy)4 dy... (81/32) tan2y/sec3y dy... I solved for...
  30. W

    Substitution for double integrals

    Homework Statement Find a transform T that maps the unit square in the u-v plane to a quadrilateral with corners (1,2), (3,3), (4,2) and (2,1) to the x-y plane. Homework Equations The Attempt at a Solution I've been able to create the proper region in the x-y plane when I have the transform...
  31. C

    Integration: Trig Substitution

    My apologies. I'm not proficient with latex, and it is bogging my computer down for some reason today. Homework Statement intdx/\sqrt{(4-x^2)} [0, 2/sqrt{2} Homework Equations Trig Identity: a^2-a^2sin^2\theta The Attempt at a Solution In the interest of my own sanity I am going to...
  32. M

    Trig Substitution Homework: Int x^2 + 36/4x^2

    Homework Statement \int\frac{\sqrt{x^2 + 36}}{4x^2}}dx Homework Equations sqrt(a^2 + x^2) substitution for x = a tan theta The Attempt at a Solution I set x = 6 tan theta x^2 = 36 tan^2 theta dx = 6 sec^2 x \int\frac{\sqrt{36 + 36 tan \theta}}{144 tan \theta}dx \int\frac{\sqrt{36(tan...
  33. A

    Trouble with Integrating \cos^{5}7x\sin7x Using Substitution

    trying to solve the following integral by substitution but having trouble: \int\cos^{5}7x\sin7xdx I attempted to set u=\cos^{5}7x and ended up with (by chain rule...which I hope is correct!): du=-35\cos^{4}7x\sin7xdx This doesn't seem too helpful but can't think of a better...
  34. MathWarrior

    Question about integration by substitution?

    I am confused about integration in other cases, I understand that you can use substitution if the derivative exists next to what your trying to integrate then you can use it. However while studying Arc Length and surface of a revolution I came across a problem such that I had to integrate the...
  35. V

    Question about trig substitution intervals

    Homework Statement my professor tell me that when looking at the case ∫ √ (a^2 - x^2) , the trig substitution of course is asinϑ where -pi/2 ≤ ϑ ≤ pi/2. What I don't understand is why my professor tells me that when this term, √ (a^2 - x^2), is in the denomenator of the integrand that we must...
  36. M

    2x2 matrix elimination / substitution

    Homework Statement I'm following an online course on linear algebra where matrix elimination was explained. They showed this for a 3x3 matrix, I wanted to test this with a 2x2 matrix but somehow managed to do something wrong.. I have two equations with 2 unknowns: 2x - y = 0 -x + 2y = 3...
  37. C

    Integrating an ODE with Substitution: How to Handle Radicals?

    I would appreciate any advice on the following ODE substitution question: xy' = y + (x^2 + y^2)^.5 Dividing thru by x and using the usual y/x substitution, I get: y' = v + (1 + v^2)^.5 but I don't know if that is right or how to integrate the left side. The book has the answer of y + (x^2 +...
  38. G

    Maple Maple 14 - substitution into Differential equation

    I'm working on a lab for my Differential Equations class where we have to use a computer graphing program to do the work for us. I have chosen to use Maple 14. So far what I have to do is graph a differential equation and find the solution to it. However, it says that I should substitute y=ax+b...
  39. K

    Repeated Substitution to solve a recurence.

    I have to solve the following recurrence but I keep getting stuck. T(n) = 1, n=0 T(n) = T(n-1) + n^2, when n>1 I start by plugging in (n-1) into the function again to get... T(n)=(T(n-2)+(n-1)^2)+n^2 Which simplifies down to (T(n-2)+2n^2-2n+1. I then do it again and get this...
  40. M

    Solving Substitution Problem: \int (x2 +2x +1)e^(-ln(x+1)) dx

    Homework Statement \int (x2 +2x +1)e^(-ln(x+1)) dx Homework Equations The Attempt at a Solution I started off by factoring the integrand into: \int (x+1)(x+1)e^(-ln(x+1)) du Then I tried to make a substitution: u=(x+1) so du=dx This left me with this: \int u2...
  41. Z

    Improper integrals and trig substitution

    Homework Statement It's been a couple of years since I've done real math, so I'm kinda stuck on this one. This is actually part of a physics problem, not a math problem - but I'm stuck on the calculus part. I'm trying to solve this guy: \int \limits_{-\infty}^{\infty}...
  42. B

    What is the Purpose of U Substitution in Solving Integrals?

    Homework Statement the integral of 1/(1-y)dy Homework Equations The Attempt at a Solution ln|1-y|+C however I believe you use u substitution as 1-y=U? Why is this so?
  43. K

    Calculating Sphere Volume Using Trig Substitution

    Homework Statement find the volume of a sphere of radius R by integrating over the primary volume elements in cartesian coordinates. Hint: use a trig substitution for your integral over dy Homework Equations The Attempt at a Solution I don't understand what the problem wants me...
  44. L

    Solving ODE Substitution: dy/dx= (4x sec(2y/x) +y) / x

    Homework Statement dy/dx= (4x sec(2y/x) +y) / x IC: y (1) = pi/4 Homework Equations The Attempt at a Solution So i can split that up into 4xsec(2y/x)/x +y/x = 4sec(2y/x) +y/x and let v= y/x dy/dx = xdv/dx +v 4sec(2v) +v = xv' +v 4sec(2v)=xv' which is...
  45. C

    What is the best substitution for solving this ODE?

    So I am trying to figure out what substitution to use for the following ODE substitution: x^2*y' + 2xy = 5y^3; I initially moved the 2xy to the right but to no avail because when I tried to divide through by x^2 (to clear the left), I struggle to get the y/x format on the right. If the...
  46. V

    Another trig substitution question

    Homework Statement sorry wait a few moments for the details, i hit post on accident prematurely ∫ √(1 + x^2)/x dx The Attempt at a Solution ∫ √(1 + x^2)/x dx x = tanϑ , dx sec^2ϑ dϑ -π/2 < ϑ < π/2 √(1 + x^2) = secϑ ∫ (secϑ * sec^2ϑ dϑ )/ tanϑ dϑ after using trig identities...
  47. V

    Question about where to start this trig substitution integral

    Homework Statement ∫ x^2√(a^2 - x^2) dx evaluate integral from 0 to a Homework Equations The Attempt at a Solution so i know the format of this problem requires the substitution of asinϑ -π/2 ≤ ϑ ≤ π/2 , but i don't know how to change the bounds of the integral...
  48. V

    Trig substitution integral(need a check on the solution)

    Homework Statement this is the first problem like this I've ever tried so take it easy!:redface: evaluate the integral I = ∫ x^3/√(16-x^2) dx from 0 to 2√3 The Attempt at a Solution - π/2 < ϑ < π/2 x = 4sinϑ , dx = 4cosϑdϑ *x = 2√3, x/4 = sinϑ , sinϑ = √3/2 , ϑ = π/3 x = 0 sinϑ = 0...
  49. H

    Integrals using u substitution

    Homework Statement Using substitution, find the integral of 32x2/(2x+1)3 Homework Equations The Attempt at a Solution I initially tried plugging u in for 32x2 but that wouldn't work because it won't cancel out with the problem below it anyway. I'm pretty sure we are not expected...
  50. W

    Need a Few Hints for Substitution

    I've been doing Calculus examples using substitution recently, and some are very easy to spot when to make what u, but sometimes it's not that easy. I'm having trouble determining which equations I should make as u, and which ones I shouldn't. I would greatly appreciate it if I could be given...
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