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. L

    U substitution on ∫sin(x^5)dx

    Homework Statement Use Part 2 of the Fundamental Theorem of Calculus to find the derivative. \int_3^x sin(t^{5}) \, dt Homework Equations The Attempt at a Solution I know the general idea of what I'm supposed to do as far as evaluate the indefinate integral and then do a subtraction of the...
  2. J

    Integration by substitution - I'm stuck

    θHomework Statement I'm trying to do an integration by substitution, but I'm completely stuck at the moment ∫(1-sin2θ)cosθ dθ Homework Equations ∫u dv = uv - ∫v du The Attempt at a Solution u = 1 - sin2θ dv = cosθ dθ du = -2sinθcosθ or -sin(2θ) v = sin I found du as...
  3. B

    Cracking a monoalphabetic substitution cipher

    I am trying to break a harmless ciphertext that uses a monoalphabetic substitution cipher. The ciphertext is exactly 244 characters long, without any spaces between words. It consists only of uppercase letters. ciphertext =...
  4. M

    Integration via substitution

    Homework Statement Integrate the following via substituion: t = r(r2 -4)5[/sub] The Attempt at a Solution I tried numerous variations. I tried substituting in u = r^(2/5) -4r^(1/5) also u=r^2 -4 and u = r^(11/5) -4r^(1/5) NONE of these substitutions worked because of the lone r...
  5. C

    Economics: Elasticity of substitution between capital and labor

    Homework Statement Am I right or wrong on the following? The more capital is needed to replace one unit of labor to attain the same production level, the lower the elasticity of substitution between capital and labor. It can measure how productive the capital in question is, and/or how...
  6. M

    Integration involving trig. substitution

    Homework Statement See below. 2. The attempt at a solution Hey there, apologies for doing so, but I don't know how to use latex on this board (it doesn't show me anything when I hit preview, so I had to make a picture for the sake of cleanness. imgur.com/WzrAR.png The first line is the...
  7. J

    MHB Is the Integral of 1/sqrt(1-x^4) Expressible in Terms of Elementary Functions?

    $\displaystyle (3)\;\; \int \frac{1}{\sqrt{1-x^4}}dx$
  8. L

    Need help solving this indefinite integral via integration by substitution

    Homework Statement Calculate the following integral: \int{\frac{\sqrt{x+1}}{x+5}dx} \ , x ≥ 1 By using the following substitution: t=\sqrt{x+1} Homework Equations Well using the integration by substitution formula. The Attempt at a Solution So I have t=\sqrt{x+1}...
  9. J

    Proof d/dx e^x=e^x using substitution

    Homework Statement Proof d/dx e^x=e^x, use e=limit (1+1/h)^h h->infinity Show how that implies d/dx e^x=e^x t Homework Equations The Attempt at a Solution Ive tried using chain rule--wasnt accepted Also, I did e=(1+h)^[1/h]-->e^h=1+h, then reduced to e^x, still didnt accept...
  10. T

    Variable substitution in Langevin equation and Fokker-Planck equation

    Dear all, I have a question about the variable substitution in Langevin equation and Fokker-Planck equation and this has bothered me a lot. The general Langevin equation is: $$\frac{dx}{dt}=u(x)+\sqrt{2 D(x)}\eta(t)$$ and the corresponding Fokker-Planck equation is thus: $$\frac{\partial...
  11. O

    Small trig substitution problem.

    Homework Statement I was working on a problem set involving greens theorem and I came across this peculiar trig substitution. I was just wondering how it came about as I couldn't find anything like it on Wikipedia's page. sin^4(t)cos^2(t) + cos^4(t) sin^2(t) = cos^2(t)sin^2(t) The...
  12. D

    Substitution Polymers: Research, Explanation and Help Needed

    Hello, everyone. So, this is my first time doing Chemistry at school and today my teacher assigned each student a topic in Chemistry to research and give a short presentation on it on Monday. He assigned me the topic of, Substitution Polymers. So, tonight I thought I might do some research on...
  13. M

    MHB Question about Trigonometric Substitution

    Hello again, I have a question about a trigonometric substitution problem that I am struggling with. I was able to get the correct answer, which I know is correct because of Wolfram verification, and my school has a way of showing an example which showed the steps... Anyway, see below...
  14. Sudharaka

    MHB Substitution to solve fourth order diff equation

    pete078421's question from Math Help Forum, Hi pete078421, Using the given substitution you get, \[\frac{d^2z}{dt^2}+2z=4t^2\] First we shall find the complementary function for this differential equation. The auxiliary equation is, \[m^2+2=0\] \[\Rightarrow m=\pm i\sqrt{2}\] Therefore...
  15. L

    Differential equations substitution problem

    Homework Statement Solve using an appropriate substitution ydx+(1+ye^x)dy=0 Homework Equations N/A The Attempt at a Solution u=y du/dx=dy/dx u+(1+ue^x)du/dx=0 This is where it gets really sticky for me. I can't see it being a separable variable problem because it seems...
  16. R

    Is U Substitution the Key to Solving Tricky Integration Problems?

    Homework Statement The Attempt at a Solution if x2 = u - 1, and if x3 = x2 * x, then x3 should equal (u-1)x, not .5(u-1). I'm assuming that they got u.5 because (x2+1).5 = (u-1+1).5 which is the same as u^.5
  17. R

    U substitution and integration by parts

    I would think because of this The following problem: At this stage they should use integration by parts: However, maybe integration by parts is only useful when one of the parts is e^x ln or a trigonometric formula.
  18. madmike159

    Integration by substitution problem

    Homework Statement Using a suitable substitution find the solution to: ∫ (x+2)50(x+1)dx Homework Equations The Attempt at a Solution I can't find a solution to this using substitution. Wolfram alpha give an answer that is too long to be calculated by hand. Can anyone work...
  19. F

    Integral involving trig substitution

    Hello, I am trying to integrate 1/(x^2-1). Apparently this can be solved by using trig substitution involving tan ? Can someone please help me to understand how to go about it. Thanks kindly for any help.
  20. D

    How to integrate Sin(x)e^Cos(x) using substitution.

    So a question for a test I just had was integrate by substitution: Sin(x)e^Cos(x). I did something like this: Let u=Cos(x) du=-sin(x) dx ∫sin(x)e^Cos(x) dx = ∫-e^u du =∫-e^Cos(x) du...
  21. C

    Double integral with substitution

    Homework Statement Evaluate (using a substitution) \int\int_{B}x^{2}+2y dxdy where B=\{(x, y) | x^{2}+y^{2}≤4\} The Attempt at a Solution I attempted a solution using polar coordinates, so the integral becomes \int\int_{B_{ρθ}}(ρ^{2}cos^{2}(θ)+2ρsin(θ)) ρ dρdθ, and the integration...
  22. S

    Solving a Tricky Substitution with d^2x/dt^2

    Hi, Firstly: This is not a homework Q. Check my previous posts, you will see the stuff i ask is for my own genuine learning. Let: \vartheta = (\Omega*t)/2 Now I have: d^2x/dt^2 And I want to sub in for t. So: d/dt = d\vartheta/dt * d/d\vartheta (Basic chain rule) I can work out that...
  23. F

    Could molecular substitution occur?

    Suppose we lived in significantly hotter conditions that what we live in right now (or lower pressure)... could organisms composed of Tin or Lead as opposed to carbon, Bismuth/Antimony as opposed to Nitrogen, Selenium and Tellurium as opposed to oxygen and sulfur respectively, and substances...
  24. S

    Substitution for integration of e^(x*y) dx

    Really not sure... Does anyone know an appropriate substitution? The whole problem is: Find the substitution that simplifies the differential equation x(dy/dx) + y = e^(x*y)
  25. J

    Solving equations via substitution

    I am trying to solve an equation that involves substitution. I was given k= 7 in the equation n=k+c i was also given n=2^c-1 I figured that 7+c could be substituted into the equation as n, so I got 7+c=2^c-1 and therefore c=2^c-8. The problem is that the answer I want is c=4...but...
  26. D

    Applying Green's THM, Polar Coords substitution

    Use Green's THM to calculate the line integral ∫C(F<dot> dx), where C is the circle (x-2)2 + (y - 3)2=1 oriented counterclockwise, and F(x,y)=(y+ln(x2+y2), 2tan-1(x/y)). Green's THM ∫∂SF<dot>dx=∫∫S(∂F2/∂x) - ∂F1/∂y) I tried doing it by brute force. I took the partials and put them...
  27. F

    Second order differential equation using substitution

    Homework Statement \sin\theta\frac{d^2y}{d\theta^2}-\cos\theta\frac{dy}{d\theta}+2y\sin^3\theta=0Homework Equations Use the substitution x=\cos\thetaThe Attempt at a Solution I started off by listing: x=\cos\theta\\ \frac{dx}{d\theta}=-\sin\theta\\ \frac{d^2x}{d\theta^2}=-\cos\theta\\ But...
  28. E

    Trigonometric substitution dx / (x^2(9-4x^2)^(1/2))

    The problem is to solve the integral of : dx / (x^2(9-4x^2)^(1/2)) using trig substituition, which I really don't understand. Formula's that are useful: The integral table Integral 1/(u^2(a^2-u^2)^(1/2))= -((a^2-u^2)^(1/2)) / (ua^2) Work so far: Figuratively banging my head...
  29. D

    Integration by substitution for dy/dx=(x+2y)/(3y-2x)

    Homework Statement Original problem is differential equation dy/dx=(x+2y)/(3y-2x) This is part of solving differential equation. x(dv/dx) = (1+4v-3v^2)/(3v-2) so one way of solving, I take out the negative sign x(dv/dx) = -((3v^2-4v-1)/(3v-2)) , separate and bring over...
  30. D

    Integration by substitution (and esp. Weierstrass' substitution)

    The stupid question of the day. Is it fair to say that\frac{du}{dx} = \frac 1 {dx/du} since this comes (I think) from the chain rule, \frac{dx}{du} \frac{du}{dx} = \frac{dx}{dx} = 1 Which means that, when integrating by substitution, I can choose to do either of \int f(u) du = \int...
  31. S

    Integration, u substitution with limits

    Homework Statement find ∫x/√(x+1).dx with limits 1 & 0 using substitution x = u^2 -1 Homework Equations The Attempt at a Solution dx = du x = u^2 -1 u = √( x+1) sub limits of 1 & 0 into u. Hence new limits of √2 & 1 Therefore, ∫ u^2 -1/ u = ∫ u - 1/u =...
  32. B

    Tricky Integration with Trig Substitution

    Homework Statement Evaluate. \int(4-y)\sqrt{4-y^{2}}dy I have the solution using CAS software here: 2y\sqrt{4-y^{2}}+8sin^{-1}\frac{y}{2}+\frac{1}{3}(4-y^{2})^{3/2} but I need to do this by hand. I have researched the usual trig methods but am having some difficulty. Can...
  33. S

    How do I Integrate this u substitution with limits.

    Homework Statement Find ∫e^x/ (1+e^2x). dx , with limits ln 2 & 0 given u= e^x Homework Equations The Attempt at a Solution u= e^x du/dx = e^x dx= du/e^x sub limits of ln2 & 0 → u Hence, limits 2 & 1 Therefore, ∫u* (1+e^2x)^-1* du/e^x = ∫ u/ (u + e^3x) = ∫...
  34. S

    Integration, u substitution with limits

    [b]1. Homework Statement Evaluate ∫ 3x /(3x+1)^2.dx , with limits 1 & 0 using the sustitution u = 3x+1 Homework Equations The Attempt at a Solution u= 3x+1 du/dx = 3 dx = du/3 Therefore, ∫ 3x*(u)^-2 * du/3 = ∫ x* (u)^-2 Since u = 3x +1 Therefore, x =...
  35. C

    Substitution Method on indefinite integral

    Say we are solving an indefinite integral ∫x√(2x+1) dx. According to the textbook, the solution goes like this. Let u = 2x+1. Then x = (u-1)/2. Since √(2x+1) dx = (1/2)√u du, x√(2x+1) dx = [(u-1)/2] * (1/2)√u du. ∫x√(2x+1) dx = ∫[(u-1)/2] * (1/2)√u du. <= What justifies this?? The...
  36. S

    Integration - u substitution problem (Integration by parts?)

    Homework Statement Find the integral of 3x* (2x-5)^6*dx, let u= 2x -5. Homework Equations Im not sure if i am meant to use integration by parts or not?? I was able to do previous questions of the topic just using u sub to get rid of the first x variable. The Attempt at a Solution...
  37. J

    U substitution with definite integral

    Homework Statement make a u- substitution and integrate from u(a) to u(b) Homework Equations ∫[0,1] √(t^5+2t) (5t^4+2) dt The Attempt at a Solution u= t^5+2t du= 5t^4+2 u(1)=2 u(0)=0 ∫[0,1] √(u) du (2/3)(u)^3/2+c l[0,2] (2/3)( 0^5+2(0))^3/2- (2/3)(2^5+2(2))^3/2 0+...
  38. M

    Comp Sci Using fortran to Solve linear equations using gauss elimination and back substitution

    Homework Statement What will be the value of the variable ipvt and AMD when the input value of lud to the following subroutine (solver) is zero ? subroutine Solver (A,B,N,lud,Z) integer lda,N,ipvt(1000),info,lud,IDAMAX &j,k,kp1,l,nm1,kb double precision...
  39. B

    MHB Calculating elasticity of substitution help

    Calculate the elasticity of substitution between y and x for F(x,y) = 10x^2 + 15y^2 I was able to calculate the Marginal Rate of Substitution as 20x/30y but I'm not sure how to proceed past that. The answer in the book is -1. Any and all help appreciated!
  40. J

    U substitution with trig

    Homework Statement use substitution to evaluate the integral Homework Equations 1)∫ tan(4x+2)dx 2)∫3(sin x)^-2 dx The Attempt at a Solution 1) u= 4x+2 du= 4 (1/4)∫4 tan(4x+2) dx ∫(1/4)tan(4x+2)(4dx) ∫ (1/4) tanu du (1/4)ln ltan(u)l +c 2) u=sinx du= cosx or u=x du = 1 ?
  41. H

    Calculators What Are the Best Replacement Options for the HP 32Sii Calculator?

    I need a new calculator as a replacement for my (now deceased) beloved HP 32Sii. What would be the next best thing?
  42. D

    HELP First Order DE using Substitution Method

    I feel as if I have made the correct substitution, what am I missing? See Attachment. Thanks, Dane
  43. B

    Troubleshooting Trigonometric Substitution for Circle Area Calculation

    I was messing around proving the area of a circle using trigonometric substitution. However, I ended up with area = -πr^2. In my integral I ended up using trigonometric substitution and setting x = r*cos(theta) However, this yields x = -r*sin(theta)*d(theta). When that's substituted...
  44. T

    Verifying the integral form of the Bessel equation by substitution

    Homework Statement The following is an integral form of the Bessel equation of order n: J_n(x) = \frac{1}{\pi}\int_0^{\pi}\ \cos(x\sin(t)-nt)\ dt Show by substitution that this satisfies the Bessel equation of order n. Homework Equations Bessel equation of order n: x^2y'' + xy' +...
  45. B

    Substitution of a definite integral

    Homework Statement The Attempt at a Solution I don't see why the √v disappears in this step I understand how they got the 20/3, because they integrated, but if they're integrating then I would think v^-1/2 would become (v^1/2)/(1/2)
  46. B

    Substitution of a definite integral

    Homework Statement Why does the 3x^2 disappear? Doesn't it play a role in the answer?
  47. B

    Simplifying the Substitution Rule for Integration

    Homework Statement here is the answer The Attempt at a Solution My book doesn't do a good job of explaining the substitution rule. here is their explanation: using the solution manual and looking at how they got the answer to other questions, I've written down my own...
  48. G

    [Integration] A tough substitution problem

    Homework Statement The following is to be evaluated using substitution or partial integration. \int\frac{(2x-1)}{e^{\arctan(x)}}\,dx (It's supposed to be e^(arctan(x)) but I'm new to LaTeX and can't quite figure out how I would input it correctly) (Fixed it for you.) Homework...
  49. C

    Chain rule or Substitution rule?

    Chain rule or Substitution rule? Homework Statement It appears that a standard result in ODE is the following: if f(x,t) is smooth enough, then the solution \psi(t) to the initial value problem: x(t)=x_{0}+\int_{0}^{t}f(x(s),s)ds x(0)=x_{0} is continuously differentiable with respect to...
  50. S

    Trig substitution: integrate sqrt(16+x^2) over x

    Homework Statement \int\frac{\sqrt{16+x^{2}}}{x} Homework Equations The Attempt at a Solution set x=4tant dx=4sec^{2}t dt so after plugging in and using a quick trig identity I get: \int\frac{16(sec^{2}t)*4sec^{2}t dt}{4tant} Then after a quick cleanup: 16*\int...
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