parts Definition and 817 Threads

Homework Statement i have to create a general formula for integral of (x^n * e^x) dx using whatever method i deem appropriate. (the only way i could think of is by parts) Homework Equations int(x^n * e^x)dx int(uv')dx=uv-int(vu')dx The Attempt at a Solution i used integration by...

Homework Statement ∫ x * e^-x dx Homework Equations Integration by parts: Just wondering if below is correct. Not brilliant with Integration by parts and not sure if my +ve and -ve signs are correct. Some help to say if i am correct or where i have gone wrong would be brilliant...

[b]1. The problem statement, all variables and given/known Homework Statement \int \frac{sinx}{x}dx Homework Equations The Attempt at a Solution Which method should work here? I tried integration by parts and it looks too much. Is there a way to solve it without approximating it with the...

Homework Statement I had this integral on my physics homework and for the life of me couldn't solve it. I ended up using Maple..well wolframalpha.com because Maple's output sucks. Anyway here is the problem. \int_{0}^{\infty} x e^{-2 \alpha x}dx Homework Equations \int u dv = uv - \int v...

In my linear algebra text it says it's possible to define (for nxn matrix A) A_1^* =\frac{A+A^*}{2} A_2^* =\frac{A-A^*}{2i} so A=A1+iA2 It then asked if this was a reasonable way to define the real and imaginary parts of A. Is there a specific convention to define the real and imaginary parts...

I would like to solve the following integral but I am unsure of the best way to solve it: \int_{0}^{H}xsin(\frac{w}{x})cos(\frac{x}{w})cosh(\frac{H}{w})dx Is it possible to use integration by parts?? Thanks in advance

Hi All, This is not a homework question, I am just trying to be come quicker at integrating by parts, when performing Laplace Transforms. My textbook gives a basic example for performing the Laplace Transform of the variable t, to the transformed variable of s for the equation...

the expression to integrate is: \int x^{3}e^{x^{2}}dx and in the spirit of "LIATE" I set my u and dv as the following: dv=e^{x^{2}}dx u=x^{3} however, doing this that I integrate dv=e^{x^{2}}dx in order to get v...and unless I'm missing something, this does not seem like an easy...

problem is to integrate the following by parts: \int x\sec^{2}xdx my feeling is convert the secant term to cosine by: sec^{2}x=cos^{-2}x\Rightarrow\int\sec^{2}xdx=\int\cos^{-2}xdx then: u=\cos^{-2}x\implies du=2\sin x(\cos^{-3}x) and also: dv=xdx\implies v=\frac{x^{2}}{2}...

problem is solve the following integral by parts: \int\ln(2x+3)dx I used substitution: u=ln(2x+3) \Rightarrow du=\frac{2}{2x+3}dx and for dv: dv=dx \Rightarrow v=x however, once I plug all these into my integration by parts formula, I get: x\ln(2x+3)-\int\frac{2x}{2x+3}dx and this new...

Hi -- I want to integrate this integral and ask if my work is correct or not. \int^\infty_0 dx x^{\alpha-1} e^{-x} (a+bx)^{-\alpha} ---------- I want to integrate it by parts, so I have (a+bx)^{-\alpha} = v -b\alpha(a+bx)^{-\alpha-1}dx = dv x^{\alpha-1} e^{-x} dx = du...

I am taking calculus b but for some reason it seems to be a shorter version according to my instructor. We are using james stewart 6th edition but only taking chapters from 7-11 excluding 10 which are 7_Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions...

Homework Statement ∫ ln(2x+1)dx Homework Equations The Attempt at a Solution ∫ ln(2x+1)dx 1/2∫2ln(2x+1)dx t = 2x+1 dt = 2dx 1/2∫ln(t)dt u = ln(t) du = 1/t dt dv = dt v = t tln(t) - ∫ t*1/t dt tln(t) - ∫ dt tln(t) - t 1/2*[(2x+1)ln(2x+1) -...

Homework Statement I don't know why, but the partials are really confusing me here. I need to integrate the following expression in a derivation: I = \int_0^\delta v(x,y)\frac{\partial{u(x,y)}}{\partial{y}}\,dy \qquad(1)Homework Equations I am supposed to integrate by parts here. \int...

Homework Statement integral of x^2ln(x)dx Homework Equations The Attempt at a Solution u=ln(x) du= 1/x dv=x2dx x^3/3 integral x^2ln(x)dx = ln(x)x^3/3-intergral(x^3/3)(1/x)

hello, i am stuck on how to do this I know how to do it for an indefinite integral, but it gets confusing for a definite integral. from my knowledge, when doing a definite integral, you have to change the upper and lower limit. but when it comes to integration by parts for a definite integral...

Homework Statement \intx^2tan^{-1}xdx The Attempt at a Solution \int{x^2tan^{-1}xdx} \int{x^2tan^{-1}xdx} = \frac{x^3}{3}tan^{-1}x-{\frac{1}{3}}\int \frac {x^3}{1+x^2}dx let {}u=1+x^2, \frac{du}{2}=xdx \frac{x^3}{3}tan^{-1}x- \frac{1}{6}\int (1-1/u)...

Homework Statement \int t sin(2t) dt Homework Equations Integration by parts formula: \intudv = uv - \intvdu The Attempt at a Solution I chose t to be u so, u=t du=dt dv=sin(2t)dt v=(sin)^2 (hope that's right. I used double angle formula to change sin(2t) into 2sint...

Homework Statement I have work these two problems, but in the first one #4 I feel like I'm missing something a step or something. and in the second problem I'm just lost, I can't finish it so will you please assist me. your help is appreciated. Homework Equations thanks a lot. The...

I'm looking for a 3d modeling software that let's me interact with rivets and joints to see how it would move. Basically I want to design a contraption made out of wooden slats and hinges/joints that open and folds into certain shapes. I would prefer software with a very low learning curve. Also...

Homework Statement Is this true or false? \int_V {\vec \nabla \Phi \bullet {\bf{E'}} \cdot {d^3}x} = \vec \nabla \Phi \bullet {\bf{E'}} - \int_V {\Phi \cdot \vec \nabla \bullet {\bf{E'}} \cdot {d^3}x}

Homework Statement I have to solve this integral S cos(x^1/2)dx where S is the integral symbol Homework Equations The Attempt at a Solution the book tells me to use substitution and then integrate by parts so i say u = x^1/2 du = 1/2*x^-1/2 then i can write 2 S...

Homework Statement Solve the integral of [xln(x^2+9)] wrt x using the tabular method. Homework Equations By parts using the tabular method. The Attempt at a Solution u: 1. ln(x^2+9) 2. 2x/(x^2+9) dv: 1. x 2. (1/2)x^2 3. (1/6)x^3 The answer for now is ...

Homework Statement Hello. I am doing some problems on integration by parts and got stuck on the following problems. Any help would be appreciated. i. \int \arcsin x dx ii. \int_{0}^{1} x \ln (9+x^2) dx iii. \int x^2 \arctan x\, dx Homework Equations u\,du=uv-v\,du The Attempt at a...

[PLAIN]http://img25.imageshack.us/img25/8933/lastscante.jpg I am new to integration by parts and am not sure what boundries to use when eveluating v on the bottom right.

Homework Statement The definite integral of from 0 to 1 of ∫ (r3)dr/sqrt(4+r2)Homework Equations ∫udv = uv - ∫vdu ∫du/sqrt(a2 - u2) = arcsin(u/a) + C ∫du/(asqrt(a2 - u2)) = (1/a)arcsec(u/a) + C The Attempt at a Solution I made u = (4+r2)-1/2 because I thought it easier to get it's...

Homework Statement Integrate: \sqrt{x}e^\sqrt{x}Homework Equations See aboveThe Attempt at a Solution Well I started off first by taking t=sqrt(x) but that didn't get me very far. So then I decided to make x equal to t^2 which sort of worked. After hours of struggle I decided to have a look at...

is the following formula of integration by parts \int_{-\infty}^{\infty}dxf(x)D^{n}g(x) = (-1)^{n} \int_{-\infty}^{\infty}dxg(x)D^{n}f (x) valid for real or non-integer n? the problem i see here is the term (-1)^{n} , which may be not so well defined for non-integer 'n'

Homework Statement Homework Equations The Attempt at a Solution I tried this problem and couldn't figure it out so I went and got the solution. However, I don't understand step 6 of the solution. I'm not sure how (n-1)\int\sin^{n-2}x(1-\sin^2x)dx=(n-1)\int\sin^{n-2}dx-(n-1)\int\sin^nx dx

Homework Statement dy/dx = e^ysin^2x/ysecx Stewart 6e 10.3 # 8 Homework Equations The Attempt at a Solution ydy/e^y = sin^2xdx/secx e^-ydy = sec^-1xsin^2xdx Integration by parts u = e^-y du = -e^-y dv = ydy v = y^2/2 ∫udv = e^-yy^2/2 + ∫y^2/2e^-y = y^2/2e^y +...

Hi, I have a problem on how to convert the imaginary parts of expression into all real parts. For example: x1 = - (a + ib) x2 = (a + ib) x3 = - (a - ib) x4 = (a - ib) My question is that how to express x1, x2, x3 and x4 in terms of real parts only without imaginary parts. I have used...

Homework Statement find the integral of cot^(-1)of (5x) Homework Equations Integration by parts The Attempt at a Solution u = x du = dx dv = cot ^ (-1) v = ? and then i would plug into equation [uv- integral of vdu ]

Homework Statement My homework problem is the double integral of y/1+xy dxdy. It is a definite double integral and both integrands have the values of a = 0 and b = 1. Homework Equations Integration by parts: uv - int(vdu) The Attempt at a Solution My first step of the double integral is I...

Homework Statement Calculate: \integral \frac{1}{(x^2+1)(x+1)} Homework Equations \integral f(x) g'(x) = f(x) g(x) - \integral f'(x) g(x) + C The Attempt at a Solution I've tried using both 1/(x+1) and 1/(x^2 + 1) as dv, but both end up in another integral I can't solve, one...

Homework Statement The shell of a shotgun, after being fired, with a velocity of v=1000 m/s gets split into two parts with equal masses. One of the two parts continues to move on the same direction as the whole (not separated) shell did, with a velocity of v=1500 m/s. a) Find the velocity...

Homework Statement Given characteristic functions f and g on the intervals [1,4] and [2,5] respectively. The derivatives of f and g exist almost everywhere. The integration by parts formula says \intf(x)g'(x)dx=f(3)g(3)-f(0)g(0)-\intf'(x)g(x)dx. Both integrals are 0 but f(3)g(3)-f(0)g(0) is...

Homework Statement Given that the probability of finding a 1s electron in a region between r and r + dr is: P = \frac{4}{a_{0}^{3}}r^{2}e-2r/a0dr work out the probability that an electron would be found within a sphere of radius: i) a0 Homework Equations The Attempt at a...

Homework Statement Indefinite Integral (x^3)(e^x) Homework Equations The Attempt at a Solution I know I need to substitute t=x^2 t^(3/2)e^sqrt(t) U=e^sqrt(t) du=e^sqrt(t) dt dv=t^(3/2) V= (5/2)t^(5/2) Because it has an exponential function, I know I need to use the...

Homework Statement Hi This is something i don't remember what I'm supposed to do. So anyway here goes. For example if my function was xe^yx and i wanted to integrate with respect to dx then i do an integration by parts with these variables: u = x dv = e^yx now my question...

Pardon my use of the program! I am new to Physics Forums! Homework Statement EVALUATE The Integral of: Square root of (x^2 + 2x) The Integral of: x * Square root of (x^2 + 7) Homework Equations Integrating by Parts Method The Integral of udv = u*v - the integral of v*duThe Attempt at a...

Homework Statement I have been asked to find a recursive formula for the number of parts of a cuboid after n cuts, and then prove my formula. The Attempt at a Solution I have through a 3D drawing program figured out a the number of parts after 8 cuts cuts, parts 1,2 2,4 3,8 4,15...

How Can i built carbon fibre parts at home work shop?

I'm trying to start a project that uses miniature parts, solenoid valves and pumps mainly. It is very hard if not impossible to find these parts. I did manage to locate some parts that are seemed suitable for my needs. But, these parts are from some wholesale distributor. What I would like to...

integral of xarcsinx dx integration by parts and a trig sub by parts I get (x^2)/2 arcsinx - integral (x^2)/sqrt(1-x^2) after that trig sub and i get integral of sin^2 then I used the double angle identity so integral of 1/2 - the integral of (cos2)/2 so i get 1/2...

Homework Statement Evaluate integral of e2ysin(2y)dy using integration by parts.Homework Equations integral udv = uv - integral vdu The Attempt at a Solution I tried applying the above equation several times, but the integral and derivative of both e2y and sin(2y) will always have a y in...

how would i go about finding the definite integral of this (x^3*e^(x^2))/(x^2+1)^2

\int_0^\infty \lambda x e^{-\lambda x} dx How do I use the limits (infinity and 0) after getting the equation from integration by parts?

in E = E_0exp i(k dot r - wt) or E = cos(k dot r - wt) what does k dot r physically represent? Can r be any position in space or must it lie on the wave? (I physically understand what a dot product is)

We know the formula is \inline{\int udv=uv-\int vdu} but when you say that for example, dv=e^x dx, then why when you integrate to get v, you don't include the integration constant? For this integral: \int xe^{x}dx dv = e^x dx v = e^x + C?

Homework Statement \int arctan(4t) Homework Equations I know what the answer is to the problem but when i look at the solution i have no idea how they get from one step to the next. The Attempt at a Solution once we integrate by parts we get 1/4 U arctan(U) - 1/4 \int U/1+U^2...