Substitution Definition and 797 Threads

Homework Statement a) Show that: \int_{0}^{\pi} xf(sin (x))dx = \frac{\pi}{2}\int_{0}^{\pi} f(sin (x))dx [Hint: u = π - x] b) Use part a) to deduce the formula: \int_{0}^{\pi} \frac{xsin(x)}{1 + cos^2 (x)} dx = \pi\int_{0}^{1} \frac{dx}{1 + x^2} Homework Equations \int_{a}^{b}...

Homework Statement \int_0^∞ x^2exp(-x/2) dx Homework Equations The Attempt at a Solution Using u substitution: u = x/2 du = 1/2 dx \int_0^∞ 4u^2exp(-u) du*2 = 8 \Gamma(3) = 8*3! = 48 But the correct answer is 16 when I plug it in Wolfram's definite integral...

How do I solve the DE \dot{y}=\frac{t+3y-5}{t-y-1} I tried using a substitution of the form u=ax+by+c, however was unsucessful. Any suggestions?

The problem: The definite integral of [(x^2sinx)/(1+x^6)]*dx on the interval -∏/2 ≤ x ≤ ∏/2 I need help figuring out what the u should be for substitution. I've been trying to make the (1+x^6) my u, but I don't know if this is what I should be doing.

Im trying to take the integral, using substitution, of \int_0^1\frac{2\pi i[cos(2\pi t) + isin(2\pi t)]dt}{cos(2\pi t)+isin(2\pi t)} So I set u=cos(2\pi t)+isin(2\pi t)du=2\pi i[cos(2\pi t) + isin(2\pi t)]dt Yet when I change the endpoints of the integral I get from 1 to 1, which doesn't make...

Why doesn't substitution work to find 0∫2 sqrt(4-x^2). I kn ow you can find the integral in other ways. I am just curious why regular substitution won't work. Thank you in advance.

∫(1+x)/(1+x^2) dx = ... I have tryed multiple time using u substitution letting u = 1+ x... 1 + x^2... x ..x^2 but I can't get any of them to work.

I can't figure out how aromatic substituents effect aromatic rings. I can think of it in a couple ways: Is the group ortho or meta directing? When we learned about aromatic electrophilic substitution, we obviously learned about these groups. When an aromatic proton is lost, it will be...

Hi dear All Sorry for a stupid question, but I am really newbe in M. I have some function, for example D[y[r],r]. Now I want to substitute y[r] to Sin[r] and to ask Mathematicato make all the calculations. (i.e I want to get Cos[x]) If I make smth like D[y[r],r]/.y[r]->Sin[r] or D[y[r], r]...

Hi, I'm new to integration and I'm trying to figure out where I went wrong on this question. I'm close to the answer, but I can't tell where I've gone wrong? Can anyone help? Thanks. Homework Statement Q. Evaluate the following: The Attempt at a Solution Please see attachment.

Homework Statement I have the integral \int sin(2.13\sqrt{x}+2.4)\,dx I'm supposed to use the substitution y=2.13\sqrt{x}+2.4, aka. \sqrt{x}=\frac {y-2.4}{2.13} to gain the following description of the integral: \int sin(2.13\sqrt{x}+2.4)\,dx = E cos(y) + F\int y sin(y)\,dy I have...

Homework Statement Find the indefinite integral by substitution. ∫2x/(x+5)^6 dx Homework Equations The Attempt at a Solution I know how to do this using the method of partial fractions, but the book says to use substitution. Is there a way to just do a basic u-substitution...

2 Questions here! (I'm not exactly sure if it's allowed, but I want to avoid posting too many threads) Homework Statement 1)Find the following definite integrals by using a trigonometric substitution: d)1/2∫1dx/(√(2x-x2) Homework Equations x=asinu The Attempt at a Solution From...

Homework Statement I have attached the question Homework Equations The Attempt at a Solution I think the answer is no solution because there is 5 variables but only 3 equations. Is that correct?

Homework Statement 8) How might you prepare each of the following molecules using a nucleophilic substitution at some step? a) (CH3)3-O-CH3 b)CH3CH2CH2CH2CN Homework Equations none The Attempt at a Solution I'm really not sure what's being asked. I'm going to assume that I...

Homework Statement Find the particular solution to the differential equation (x + y - 4)dx - (3x - y - 4)dy = 0 that satisfies the initial condition y=1 when x=4 Homework Equations The Attempt at a Solution It's not a homog. or equal D.E., therefore I think it's substitution. I don't really...

Consider the following reaction: RCOO-COR + R'-OH → RCOO-R' + RCOOH (where -R is an alkyl group) In above reaction the acid anhydride and an alcohol forms ester and carboxylic acid. The acid anhydride used in this case is a symmetrical on that is containing only one alkyl group (R)...

Homework Statement ∫ 1/(x√(25-x^2)) dx Homework Equations by trigonometic substitution I got the following equations x = 5 sin θ dx = 5 cos θ dθ √(25-x^2) = 5 cos θ θ = sin^-1 (x/5) The Attempt at a Solution I solved it and got the following (so far, it is okay with wolfram...

Hello all, We've just begun integration in my maths class and I have a question about a certain aspect of integration by substitution. Let's say for instance you let u = 2x-1. Then you differentiate it and get du/dx = 2. My maths teacher said " you can now think of it as multiplying...

Hi, I'm really close to deriving something that many biology textbooks like to skip: the probability of a certain DNA molecule (base) remaining the same while it suffers changes both to and from the other 3 types of DNA molecules. This sounds specificially biological, but as probably a good...

Homework Statement Show that the differential equation: sin(theta)y'' + cos(theta)y' + n(n+1)(sin(theta))y = 0 can be transformed into Legendre's equation by means of the substitution x = cos(theta). Homework Equations Legendre's Equation: (1 - x^2)y'' - 2xy' + n(n+1)y = 0 The Attempt at a...

Homework Statement \int^2_1 6x\sqrt{x-1}dxHomework Equations The Attempt at a Solution Let u=x-1. Then, u+1=x, and du=dx. Continued from problem statement, =6 \int^1_0 (u+1)u^{\frac{1}{2}}du =6 \int^1_0 u^{\frac{3}{2}} + u^{\frac{1}{2}}du =6(1^{\frac{3}{2}} + 1^{\frac{1}{2}}) =6(2) =12 My Web...

Hi , I solved \int (1/((\sqrt{(x^2)+(a^2)}))^(3/2)*dx) using the substitution x = a*tan(\varphi I wonder if there are other methods to solve this problem? * (2/3) is the power on the radical function

I need to find a 1 parameter family of solutions to: \frac{dy}{dt}=-\frac{1}{t^{2}} - \frac{y}{t}+y^{2} By making the substitution: y=\frac{1}{t}+u and then reducing it to a Bernoulli equation in u. I first took the derivative of the substitution. \frac{dy}{dt}=\frac{1}{t^{2}}+\frac{du}{dt}...

Solve y' = y/x + 1/y I get a similar answer to the correct one but I believe I am making a substitution error. Here is my attempt: dy/dx = y/x + 1/y set v = y/x equation now becomes: v + x(dv/dx) = v + 1/(x*v) reduces to: dv/dx = 1/(x^2 * v) Now the equation is...

Okay, I'm going insane. I have these problems completely worked out and have stared at them for centuries but the online homework is still telling me they're wrong. Could anyone here take a look and let me know? I'd appreciate it a ton. [SIZE="4"]Problem 1: Exact Equation Homework...

Homework Statement My book has given me this example, with a step by step, but one of the steps have left me dumbfounded, they seem to have left a huge gap in steps.. Homework Equations The Attempt at a Solution \int sin^{5}xdx \int sin^{4}x sinx dx \int (1-cos^{2}x)^{2}...

Can anyone explain Weierstrass substitution? When would one use it and why? Examples?

okay so I just have a question about using substitution when solving limits. Say I have the function sinx/x, if i want to find the limit when x--> 0 using approximation ( i know how to prove it with the pinching theorem by the way). So if I substitute 0.0000000001 rad into the function i get...

Homework Statement I am asked to prove the following statement is correct integral (sqrt(a^2+x^2))/x dx = sqrt(a^2+x^2)-a log(a (sqrt(a^2+x^2)+a))+ C Homework Equations x = atanθ dx = (asecθ)^2 tan^2+1 = sec^2 The Attempt at a Solution got down to a (sec^2 θ a(√sec^2)dθ)/atanθ...

Homework Statement \int x/sqrt{(x^{2}+4)} Homework Equations x=2tanx The Attempt at a Solution x=2tanx \int2tan\vartheta/\sqrt{tan^2\vartheta}+4 2/2 *\inttan/sec \intsin=-cos now is the part where i am stuck i know from using substitution that the answr should be...

Homework Statement (i) find \int^{X}_{0} xe^{-x^{2}} dx in terms of X. (ii) Find \int^{X}_{0} xe^{-x^{2}} dx for X= 1, 2, 3 and 4. Homework Equations - The Attempt at a Solution (i) \int^{X}_{0} xe^{-x^{2}}dx -x^{2} = X dX/dx=-2x hence -1/2 dX = xdx so, -\frac{1}{2}...

first off, i can solve this problem easily with u-sub but the question asks to use trig sub. \int4x/(x2+1) then i have x=tan(theta) dx=sec2(theta) =\int4tan(theta)sec2(theta)/(tan2(theta)+1) =\int4tan(theta)d(theta) =-4ln(cos(theta))=-4ln(cos(arctan(x))) thanks for the help...

Please help me calculate these integrals. Suppose that ∫f(t)dt=11 [0,1]. Calculate each of the following. A. ∫f(4t)dt [0,0.25] = B. ∫f(1−4t)dt [0,0.25] = C. ∫f(3−8t)dt [0.25,0.375] = I did the first one and I believe is right and I try to do the 2nd and 3rd one similarily and...

Homework Statement Integral of d.cos j with regard to d.sin j Where d is a constant. Homework Equations The Attempt at a Solution I don't know how to approach this. I can substitute u=d.sin j Then I have Integral of dz/dj with regard to dz, but not sure where to go from here. Any help...

I have been spending a few days reviewing parts of College Algebra from College Algebra, by Aufmann, Barker, & Nation. I am following the discussion of the shape, features, and equation for an ellipse, and I understand the derivation well, EXCEPT that I do not know how the subsitution of b2 =...

I'm confident in my math ability, but how is it that by using the chain rule... W_{x_1 \rightarrow x_2} = \int^{x_2}_{x_1} m \frac{dv}{dt} dx can be turned into W_{x_1 \rightarrow x_2} = \int^{x_2}_{x_1} m \frac{dv}{dx} \frac{dx}{dt} dx = \int^{v_2}_{v_1}mv dv ? I understand the...

Homework Statement \int\left(1+x^{2}\right)^{\frac{3}{2}}dx Homework Equations The hyperbolic functions. The Attempt at a Solution We've been going over hyperbolic substitutions in class so I assume I'm meant to use one of those, but I'm just not sure how to choose which one. Any help...

Homework Statement the amount of nitrogen dioxide, a brown gas that impairs breathing, present in the atmosphere on a certain day in may in the city of long beach is appoximated by: A(t) = ((544) / (4 + (t - 4.5)^2) + 28 t is on interval [0, 11] where A(t) is measured in pollutant...

Homework Statement find the integral from 0 to ln2 of (e^x-1)/(e^x+1) Homework Equations The Attempt at a Solution I really didn't know what to do, but the book had a hint suggesting i multiply the numerator and denominator by e^-x and then use an appropriate substitution...

Homework Statement find the integral from 1/3 to 1/2 of 1/x(x+1)(x-1)(x^2+1) Homework Equations The Attempt at a Solution expanded and simplified: 1/x^5-x it gives a hint suggesting i use a substitution here, but i can't find an appropriate one.. Help?

Homework Statement Use the method of trigonometric substitution to evaluate the following: [SIZE="3"]\int\frac{x^{2}}{\sqrt{4-9x^{2}}} Homework Equations The only relevant equation that I could think of for this one was the trig identity: [SIZE="3"]sin^{2}\vartheta +...

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...

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...

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...

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

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 =)

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...

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...

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...