Integration by parts Definition and 438 Threads

Homework Statement Homework Equations The Attempt at a Solution What I am unsure of is how to find the derivative of u. Since the original integral is integrating with respect to y, should I be finding the derivative of u with respect to y, and treat the x's as contants?

Homework Statement Use integration by parts to prove the reduction formula: http://img214.imageshack.us/img214/1234/24206074.jpg Homework Equations The Attempt at a Solution what confuses me about this question is that its not in the form sqrt(a2 + x2) but its in ^n instead of...

Homework Statement Here is a question I'm struggling with. I encountered it in a paper, and although a solution is provided I'm not so sure I understand where they're coming from. Homework Equations \int_{r_1}^{r_2} \overline{v}\frac{1}{r}\frac{d}{dr}(r\frac{du}{dr})rdr where...

Homework Statement intergral from pi to 0. of (sin(3t)dt)^4 The Attempt at a Solution okay so i know how to do this but when i tried substitution putting 3t=u and (1/3)du= dt i always came with the the wrong coefficient at the end with the answer and so i would multiply it...

Homework Statement I'm getting different results when choosing my u & dv for Integration by Parts on the following integral: \int 2x^3 e^x^2 dx (Note, the exponent on 'e' is x^2) This yields the correct solution: u = x^2 dv = 2x e^x^2 dx du = 2xdx v = e^x^2 However, I have tried using...

Homework Statement The method to use to integrate the function is up to us. The choices are: 1) U-substitution 2)Integration by Parts 3)Trigonometric integrals 4)Trigonometric substitution 5)Partial fraction Homework Equations According to me, the best way to do it is to use...

Homework Statement Use the method of cylindrical shells to find the volume generated by rotating the region R bounded by the curves y=e1.6 x, y=e−1.6 x and x=0.6 about the y-axis. Homework Equations V=$\displaystyle \Large \int _a^c 2pix (yt - yb) dx$ The Attempt at a Solution...

Homework Statement 1.$\int x^ne^xdx$ 2.$\int \sin ^nxdx$ Homework Equations $ \displaystyle \Large \int fg dx = fg - \int gf' dx$ The Attempt at a Solution 1. f=xn g'=ex g=ex f'=nxn-1 then just plug it in the formula? i tried but i don't get the right answer.. 2. i have...

Homework Statement \int\frac{x^3}{\sqrt{1-x^2}}dx I have to use integration by parts on the above integral. Homework Equations The Attempt at a Solution u=x^3 du=3x^2dx dv=\frac{1}{\sqrt{1-x^2}}dx v=arcsin (x) =x^3arcsin (x)-3\int\ x^2arcsin (x)dx u=arcsin (x)...

the function is c = 15te-.2t the goal is to integrate it from t = 0 to t = 3 so to set up the integral i took out the 15 first so i got: 15 * integral from 0 to 3 of t*e-.2t i set u = t and so du = dt dv = e-.2tdt so v= -5e-.2t so following the integration by parts formula i got...

the problem is find the integral of xarctan(x^2)dx i set w = x^2, so 1/2dw = xdx then i plug that into the integral to get the integral of 1/2arctan(w)dw so i let u = arctan(w) and dv = dw so du = dw/(1+w^2) and v = w so then the integral of udv = uv - integral of vdu so...

Homework Statement \int\arctan(4t)dt Homework Equations The Attempt at a Solution \int\arctan(4t)dt = t\arctan(4t) -4 \int \frac{t}{1+16t^2}dt I'm stuck at this point. I think I need to make a substitution for the denominator, but I'm not sure how to go about doing so.

Homework Statement \int \ln(2x+1)dx Homework EquationsThe Attempt at a Solution u = \ln (2x +1) du = \frac{2}{2x+1} dv = dx v = x xln(2x+1) - \int \frac {2x}{2x+1}dx I'm not sure how to proceed. Do I separate the fraction in the integrand or do long division? I think I separate the...

Homework Statement \int \frac{x^3e^{x^2}}{(x^2+1)^2} The Attempt at a Solution Well, this problem is hard, so I thought to use u = x3ex2 so du = x2ex2(3+2x2) dx and dv = (x2+1)-2 then v = -2(x2+1)-1 Please check v though to make sure my algebra is right. so then using the by parts formula...

I've seen this formula stated and used, ( in a stanford university video lecture) \int \frac{dA}{dt}B\ dt = - \int \frac{dB}{dt}A\ dt with the condition that you don't vary the end points. but i don't understand how you can just remove the AB term from the right hand side, and I've...

Homework Statement Find or evaluate the integral using substitution first, then using integration by parts. \int \ln (x^2 + 1) \, dx The Attempt at a Solution Let \: u = x^2 + 1 du = 2x \, dx dx = \pm \frac{du}{2 \sqrt{u - 1}} Then \int \ln (x^2 + 1) \, dx = \pm...

Homework Statement Find the area bounded between the two curves y=34ln(x) and y=xln(x) Homework Equations Integration by parts: \intudv= uv-\intvdu The Attempt at a Solution First I found the intersection points of the two equation to set the upper and lower bounds. The lower...

Homework Statement Integrate: -\frac{2}{\theta} \int^{\infty}_0 y e^{-2y/\theta} dy + \frac{2}{\theta} \int^{\infty}_0 y e^{-y/\theta}dy Homework Equations The Attempt at a Solution Let u = y/theta; y=u*theta; dy = du*theta, which becomes -2 \int^{\infty}_0 u \theta e^{-2u}...

What's up with this \int_{-\infty}^\infty \sin{x}\frac{1}{x}dx=\pi Now I try integration by parts \int_{-\infty}^\infty \sin{x}\frac{1}{x}dx=[-\cos{x}\frac{1}{x}]_{-\infty}^\infty-\int_{-\infty}^\infty \cos{x}\frac{1}{x^2}dx = -\int_{-\infty}^\infty \cos{x}\frac{1}{x^2}dx = \infty...

Homework Statement Evaluate the integral (e^-theta) cos(2theta) I got this as my answer e^(-theta)-sin(2theta)+cos(2theta)e^(-theta)+C But it was wrong All help is appreciated.

I've been trying to find this online, but I haven't been able to find any site that really explains it: when performing integration by parts, is there some rule or set of guidelines to determine which part of the equation is u and which is dv?

Hello :smile: I was hoping someone could help me with this integral. Homework Statement I=\int{(x^2sin(5x^3-3))}dx Homework Equations \int{(u.\frac{dv}{dx})}dx=[uv]-\int{(v.\frac{du}{dx})}dx \frac{dy}{dx}=\frac{dy}{du}.\frac{du}{dx} 3a. The first attempt at a solution...

Homework Statement Using integration by parts, integrate: (1/x^2)(lnx) dx with the limits e and 1 Homework Equations [uv]to the limits a b - the integral of (v)(du/dx) dx (sorry, don't know how to write out equations properly on a computer) The Attempt at a Solution I've...

Hi all. I've recently learned a shortcut for integration by parts, but don't know what it's called or where it comes from. The trick is to find \lambda such that f'' = \lambda f and \mu such that g'' = \mu g, providing both are constants and \lambda\neq\mu. Then \intf(x)g(x)dx =...

\int x^3cos(x^2)dx -\frac{1}{2}x^2sin(x^2)+\frac{3}{2}\int xsin(x^2)dx -\frac{1}{2}x^2sin(x^2)+\frac{3}{4}cos(x^2)-\frac{3}{4}\int \frac{cos(x^2)}{x} the last integral

Homework Statement I'm following an example in the textbook that states: http://img24.imageshack.us/img24/1672/33686252.jpg I was just wondering what happened to the 2 out the front, I would have been more inclined to think this would be the next step...

This a techniques of integration question, and I'm wondering how do you know when to use integration by parts on a problem? My book says this bout the Integration by parts procedure. If f(x) is a product of a power of x and transcendental function then we try integration by parts. Can...

1. Suppose : f(1) = 2, f(4) =7 , f'(1)=5, f'(4) = 3 and f"(x) is continuous. Find the value of: \int_{1}^{4} xf''(x)dx Homework Equations IBP formula \int u(x)dv = u(x)v(x) - \int v(x) du The Attempt at a Solution I re-wrote the IBP formula from...

Homework Statement Let F(b) be the exact area under the graph of y = x2*e-x between x=0 and x=b for b>0. Find the formula for F(b).Homework Equations int(uv')= uv - int(vdu)The Attempt at a Solution u = x2 and dv = e-x, thus u'=2xdx and v=-e-x. y= -x2*e-x - -2*integral(xe-x). = -x2*e-x...

Why is it that whenever we encounter a question which can be solved by integration by parts, we get half the function? I mean, suppose a differentiated f(x)g(x) yielded {f'(x) g(x)dx + f(x)g'(x)dx}, then why do we get only {f'(x) g(x)dx} to extract the original function (f(x)g(x)) from?

Find http://img214.imageshack.us/img214/4186/problemm.png Homework Equations udv=uv-ƒvduThe Attempt at a Solution lndx=dv (1/X)=v u=x^2+2 du= 2x^2 I looked in the solutions manual and I don't get, why do I keep picking the wrong u & dv?Can someone please show an example on how to pick the...

Homework Statement \int\frac{t^{2}}{\sqrt{2+3t}} Use integration by parts to verify the formula: \int x^{n} sin x dx = -x^{n} cos x + n\int x^{n-1} cos x dx Homework Equations The Attempt at a Solution For the first one, I attached the picture of my work on paper, as it...

Homework Statement I=\int{\frac{x^2}{e^x+1}dx} The Attempt at a Solution I tried integration by parts but that didn't work because it just became more complicated in the end. I=x^2ln(e^x+1)-2\int{xln(e^x+1)dx} Then, \int{xln(e^x+1)dx}=xln(e^x+1)-\int{\frac{x}{e^x+1}dx} It...

Homework Statement I must evaluate the indefinite integral: \int x \arctan{x} dx Homework Equations I am using the following format to perform the integration: \int u dv = uv - \int v du The Attempt at a Solution I have tried working the problem substituting x in for u and arctan...

Hi, I wonder if this hypothesis is true: Let f_n be an arbitrarily chosen n'th anti-derivative of the function f_0. Similarly, let g_n be the n'th derivative of the function g_0. Now, \int^b_a f_0 g_0 \rm{d}x=[f_1g_0]^b_a-\int^b_a f_1g_1 \rm{d}x=[f_1g_0-f_2g_1+...]^b_a+(-1)^n \int^b_a...

Integration By Parts: Need help with a step... Evaluate the integral: \int ln(2x + 1)dx I worked it out up until: Xln(2x + 1) - \int 2x/(2x + 1) dx Then the next step throws me off. I attached a scan from the solutions manual and circled the part that confused me. Could somebody...

Homework Statement \int x \frac {\partial f} {\partial x} dx where f=f(x,t) Homework Equations \int u \, dv = uv - \int v \, du The Attempt at a Solution u = x so du = dx and dv = \frac {\partial f} {\partial x} dx so v = \int \frac {\partial f} {\partial x}...

Homework Statement I(xsin^2x,x) (1/2)I(x(1-cos2x),x) (1/2)I(x,x)-(1/2)I(xcos2x,x) x^2/4-(1/2)I(xcos2x,x) u=x du=dx dv=cos2x v=sin2x/2 x^2/4-xsin2x/4+I(sin2x,x)/4 x^2/4-xsin2x/4-cos2x/8+C book is showing a diffrent solution from integrating by parts before power reduction can somone...

Homework Statement Let F(x) and G(x) be the antiderivatives of f(x) and g(x) on [a,b]. using multiple integration, show that the integral from a to b of f(x)G(x)dx = F(b)G(b)-F(a)G(a) - the integral from a to b of g(y)F(y)dy To do so, consider the double integral of a suitable function...

Homework Statement Homework Statement The Attempt at a Solution u= cos(2x) = > du= -2 sin(2x) dv=cosx(2x) =>v= 1/2 sin(2x) ?

Homework Statement I have attempted and failed solving the following integration: Integrate : e^(-x) cos x dx Homework Equations I tried using the integration by parts rule: uv - (integral) v (du/dx) dx The Attempt at a Solution I let u = e^(-x) and dv/dx = cos x...

Homework Statement integral limit 1 to 5 integral of sqrt x * lnx dx a = 1 b= 5 Homework Equations The Attempt at a Solution 2 x (-1 + 2 Log[x]) ------------------ 8 11.99604193 but its not right

Because of circumstance (my desire to graduate in 5 years or less), I've been forced to attempt Calc 2 in 2 months time online over the summer. About 75% of it is going smoothly (compared with 105% or so of Calc 1). Homework Statement I'm to solve the indefinite integral: \int x *...

Hey all! I was recently refreshing my memory of integration by parts via some personal reading when I thought, there must be a better way. Integration by parts (while creative in that it integrates the entire product rule) feels very arbitrary to what it's attempting to calculate (at least...

Homework Statement [Intgrl]ln(x^(2)+4)dxHomework Equations [Intgrl]udv=uv-[Intgrl]vduThe Attempt at a Solution [Intgrl]ln(x^(2)+4)dx, u=ln(x^(2)+4), du=(2x/x^(2)+4), dv=dx, v=x xln(x^(2)+4)-[Intgrl](2x^(2)/(x^(2)+4))dx

Formula for integration by parts: \int f(x)dx = \int u dv = uv - \int v du Use integration by parts to find the following integrals: a) \int x e^{1-x} dx b) \int_1^4 \frac {ln \sqrt x} {\sqrt x} dx c) \int_{-2}^1 (2x+1)(x+3)^{3/2} dx d) \int x^3 \sqrt{3x^2+2} dx Answers in back of the...

Homework Statement \int x^5cos(x^3) dx Homework Equations \int uv' = uv - \int u'v The Attempt at a Solution \int x^5cos(x^3) dx \frac{(x^5)*(sin(x^3)}{(3x^2)} - \int\frac{5x^4*sin(x^3)}{(3x^2)} dx \frac{(x^3)*sin(x^3)}{3} - \int\frac{(5x^2)*sin(x^3)}{(3)} dx...

I have a couple questions about a certain problem on http://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/intbypartssoldirectory/IntByPartsSol3.html#SOLUTION%2016 On number 18... 1) What is the logic behind separating x^7 into x^4 x^3 2) In the translation from dv to v, how did x^3...

Homework Statement In question 6, where does the -(0-0) part come from. The instructor did this for another question, question number 3 as well except in the other question the resulting value was a non-zero one and thus affected the answer.. any help appericiated...

Homework Statement ∫∫xy(x^2+y^2)^(1/2)dydx over the range 0 to 1 for both x and y. Homework Equations I believe that it requires integration by parts. Any help would be greatly appreciated.