parts Definition and 817 Threads

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)...

Hello, I'd like to say hi to everyone since I'm pretty new here, and I guess my first post goes directly to asking a question. Anyway, could someone here recommend me some program for designing parts of a jet or a space vehicle that resembles a delta winged jet. I'm doing this for learning...

can anyone tell me how to get the real and imaginary parts of the following function : (x+ i y)* Log( a+i b) where x, y a and b are all real numbers and i =sqrt (-1). Thanks very much

Nevermind, it's late and I realized why it doesn't work because I forgot to take into consideration that the denominator is (1/polynomial) Anyone care to explain to me how to do it the proper way? [SIZE="1"] 1. Question 1 \int (x+2)/(x²+x+1) dx The only reason I ask is because my...

Homework Statement I am trying to size parts of a boat, but I don't believe in my results. An attempt to solve one subproblem of this in a rulebook based way can be read here: http://www.boatdesign.net/forums/boat-design/rudder-scantling-31263.html Is it appropriate to bring that question...

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}...

I have this DE: \[y'' - 4y' + 8y = f(t) = \left\{ \begin{array}{l} t{\rm{ }},t \in [0,2) \\ t + 1{\rm{ }},t \in [2,4) \\ 0{\rm{ }},t \ge 4 \\ \end{array} \right.\] I have problems transforming f(t). I know that when I have a function defined by parts, I...

When there are, say, two complex numbers that are equal. What can we say about their equality? Can we say that the real part of one is equal to the real part of the other? Similarly, can we say that the complex part of one is equal to the complex part of the other? Is this what it means when...

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 Let lim n-> ∞ a_n = L. Then, let f(x) = ∑ from n=0 to ∞ of (a_n)(x^n). Show that the lim x-> 1 (1-x)f(x) = L. Homework Equations The Attempt at a Solution This one is pretty far over my head. I know at some point you're supposed to use Abel/SBP, but here is what I have so...

A very general question: What do the real and imaginary parts of a wave function correspond to physically? Cheers

The displacement of a wave traveling in the positive x-direction is y(x,t) = (3.5 cm)cos(2.7x - 124t), where x is in m and t is in sec. What are the (a) frequency, (b) wavelength (in m), and (c) speed (in m/s) of this wave? I don't know how to do this problem at all. I could use some help...

I hope can someone clarify this for me. I have a sequence f(of n) which is like this: fn(x) = 0-- if--x<\frac{1}{n+1} is = sin^2(x/pi)--if--\frac{1}{n+1}<=x<=\frac{ 1}{n} is = 0--if--\frac{1}{n}<x (the - are for spaces because I don't know how to do it. Nothing is negative) Then...

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?

I'm having big trouble when trying to figure this integral out. Please help! Integral (from 0 to infinity): ((x^2)/a)*e^[(-x^2)/2a] dx a is a constantThanks in advance!

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 x=cos^2(t) y=cos(t) (a) Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. (b) What is the length of the curve? Homework Equations Length of an Arc: integral of alpha to beta sqrt((dx/dt)^2+(dy/dt)^2) The...

please explain me..

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...

I think this is great for CNN. Dobbs was not a respectable journalist. http://www.ajc.com/business/grand-exit-for-cnns-197683.html?cxtype=rss_news_128746 Like so many pseudo-journalists on TV these days, Dobbs and his show were loaded with bias. Just check any poll of his to see how...

Hello everyone, Ok to understand the respiratory system, proper understanding of this diagram is essential. Something I don't have, so if anyone can help me with these questions I would be very greatful. Thanks :smile: http://img515.imageshack.us/img515/8923/rightbv.jpg 1. Anatomic dead...

Homework Statement Consider the resistor network shown in the figure below, where R1= 5\Omega and R2= 7\Omega . (a) Find the equivalent resistance between points a and b Req=([1/6 +1/5]+7)+12+6=(9.73)-1+18-1=6.32\Omega (b) If the potential drop between a and b is 12 V, find the...

was just curious to know what a cigarette lighter made of what metal they use in the exterior where the light comes out.what kind of plastic is used to hold the liquid?will the metal melt off if its switched on for a while? what's the difference between a $1 lighter and the $24 zippo lighter ...

Hi: Does anyone know of an explicit formula for the Real and Imaginary parts of GAMMA(1/2+I*y) as functions of y ? I know about |GAMMA(1/2+I*y)|^2 =Re(GAMMA(1/2+I*y))^2+Im(GAMMA(1/2+I*y))^2= Pi/cosh(Pi*y) but can't find anything about each of the Real and Imaginary terms...

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

I have multiple stepper motors i pulled out a printer and I can't seem to find any datasheets on anything. For example one of the motors is made by OKI and it has numbers 3Y25AE1 and QH4-4490. I have looked all over the internet and I can't find anything. If anyone knows a good idea to try it...

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...

Homework Statement Prove that Z can be partitioned as Z= 3Z \cup (1+3Z) \cup (2+3Z), where m+3Z={m_3n| n\in Z} Homework Equations The Attempt at a Solution Not sure how to start to prove this. I know it has to do with the remainder when an arbitrary integer is divided by 3, but I...

Hi all, What happens when we take the product of the imaginary parts of all the n-roots of unity (excluding 1)? I read somewhere that we get n/(2^(n-1)). How can we prove this? Thanks!

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...