parts Definition and 817 Threads

I am trying to integrate a difficult integrand. \[1/2*\int \sin(\sqrt(3)/2x)*\sec(\sqrt(3)x)\, dx\] I know that it requires to use integrate by parts. Which function do I use to for the differential and integrable?

Homework Statement Can anyone explain to me how is the left-sided drawing related to the right sided drawing? I asked the teacher but he confused me so I let it go. http://img443.imageshack.us/img443/3036/drawinge.jpg The description is this: This crane in the drawing is designed...

Homework Statement I do not know how to solve the following indefinite integral. I personally think it is very difficult and would appreciate it had someone can explain it step by step? Homework Equations / The Attempt at a Solution This integral must been solved by mix of...

Homework Statement Integrate ettdt using integration by parts.2. The attempt at a solution Seems like a very easy problem; however, I just started learning integration by parts-- didn't understand this. So the book's method: u=t...

∫ e^at. sinωt dt This is the second part of an electrical circuit DE problem from our notes (first part not required to solve the above integral) however in-between this integral and the answer our professor only told us that we would get to the answer by using integration by parts twice. I am...

Is the Reptilian Brain midbrain the same thing? I know at the top of the Spinale Cord is a little Ball and this is the Midbrain. Is this not what they call the Reptilian Brain?

Integration by parts not working for a particular integral When I attempt to use the method of integration by parts on the below integral, I don't get anywhere since I only arrive at the statement a = -b +b -a where a is the integral and b is the boundary term. \int e^{-x}\text{Cos}[k...

Hi all this is my first post hopefully i do it right. Homework Statement integrate ln^2(6x)dx The Attempt at a Solution *integral* ln^2(6x)dx u=ln^2(6x) dv=dx du=(2ln(6x))/x dx v=x xln^2(6x)-*integral*x(2ln(6x))/x dx xln^2(6x)-2*integral*ln(6x) dx u=ln(6x) dv=dx du=1/x...

Good morning engineers. I have a set of old patterns used for sand casting back in the days and I am wondering what kind of machinery parts they are. Especially, I would like to know if those are gears / cogs or something else. Any ideas? Thank you so much!

Hello MHB, I'm trying to solve this integral:\int x^2arctan(x)dx by parts : here is a litle bit of my resolution: http://i.imgur.com/dZk8M.jpg when I tried to solve the integral I named B fell into a sort of lool lool.

When integrating by parts the formula is \int{u} dv=uv-\int{v} du I understand where to get the u, and du... but where does one get the v?

Hey, so i am an electronics novice but i am very interested. I had an old itouch 2nd generation that wasnt working anymore so i decided to take it apart and i found what i think to be the main processing chip(no clue what the technical term is haha). So what i was wanting was for someone to tell...

I am trying to come up with a shape or design of a simple piston with holes that will allow fluid to flow in one direction better than the other. Very Simple shock design. I have tried tapered holes so as to speed up flow in one direction and it worked slightly but haven't quite found the...

Homework Statement ∫x3e5x2 dx Homework Equations uv-∫vdv The Attempt at a Solution I've tried this one a few times, but keep getting answers that are just out there. Could someone, if possible, work out just the beginning.

Found this challenging: A,B and C work at same speed. When all 3 of them plant a field with D, the job gets done in 5 hours. When all 3 of them plant the same field with E, the job gets done in 6 hours. The field was divided between the 5 workers in proportion to their 5 work rates, into a...

Homework Statement Consider the following integral: I=\int^{\pi/4}_{0}cos(xt^{2})tan^{2}(t)dt I'm trying to compute as many terms as possible of its asymptotic expansion as x\rightarrow\infty. Homework Equations x The Attempt at a Solution Let u=cos(xt^{2}). And...

Complex differentiable <--> real and imaginary parts satisfy C-R eqns and are cont. Say we have a complex function f(z) we can break this into real and imaginary parts: f(z)=u(x,y)+iv(x,y)In my book I am told the following:(1) f complex differentiable at z0 in ℂ --> the Cauchy Reimann...

Homework Statement ∫Bdot[∇×A]dV=∫Adot[∇×B]dV Prove this by integration by parts. A(r) and B(r) vanish at infinity. Homework Equations I'm getting stuck while trying to integrate by parts - I end up with partial derivatives and dV, which is dxdydz? The Attempt at a Solution I...

Homework Statement $$\int \frac{x}{(1-x^2)} dx$$Homework Equations Integration by parts, by substitution, etc. The Attempt at a Solution I just can't remember how to begin this integration. I tried doing integration by parts, where $$a(x) = x$$ $$a'(x) = 1$$ $$b(x) = $$ $$b'(x) =...

I'm unsure as to why only one of two mating parts are threaded? The top part is usually a clearance hole and the thread is only applied to the bottom part. Why is this so?

Ok I have to integrate -->∫cos(lnx) dx. could I use cos =U, -sinx=du, dv=lnxdx, v = 1/x I know the difference technically, but in this situation it is kinda weird. because the formula f(x)g(x)= uv-∫vdu. I thinking if they were number like 9(3) it would equal 27 so f(g) = f times G? but then...

How would you decompose a given function to its even and odd parts? let's say you have f(x)=e^ix, and would like to know the even and odd parts of it? how do you proceed? Thank you

Homework Statement Please help me understand the reason for substituting various trig identities into trig functions with powers instead of integration by parts. Does integration by parts not work on trig functions with powers, or is it just so much work that substituting trig identities to...

Homework Statement Are there any sample problems worked out for trig functions of higher powers which are integrated by reduction formula? Like cos^8 or cos^10 or even just cos^6 or maybe?

I'm currently enrolled in a PhD program in control systems engineering. I'm wondering what tends tend to be the most useful subsets of this field, and consequently the most important to be well-versed in. I've read Kalman filters are very important in real world applications. Optimal Control and...

Is the Right Atrium and Left Atrium the same size?

The most serious challenge to engineering a quantum computer is protecting it from decoherence. But FMO proteins in photosynthetic complexes can exhibit entanglement for a few picoseconds as reported here and here, among other places. So would it be possible to build a working, useful quantum...

I figure this problem will not be easily solvable which is why I'll ask. Basically a moving mass M with a velocity along the x direction of .5c explodes into two fragments. Fragment A moves to the -x and fragment B moves to the +x. The sum of the mass is 1/4A + 3/4B = M. What are the final...

If you look at the Human Brain and you see the Brain Steam can you see the Pons on\f the Brain Steam or is this part very close to the bottum of the Brain? I ask because some Models show it and other do not but in real life can you see the Pons of the Brain Steam?

Homework Statement αh=α-ε+ih ΔαH/Δα= dαH/dα = d/dα x (α-ε+ih) = 1-(dε/dα)

Homework Statement Evaluate the following indefinite integral: ∫(sin(ln16x))/xdx Homework Equations The Attempt at a Solution let u = ln16x therefore du=16/16x=1/x ∫sinudu =-cosu =-cos(ln16x) Why is this showing as the wrong answer?

Homework Statement Hi , I am reading a little on introductory QM , initial chapters on waves. They have given an integral for a wavepacket , assuming at t= 0. Which is: ψ(x,0) = \int A cosk'x dk' (I don't know how to define limits to the integral in Latex upper = k+Δk , lower limit =...

Homework Statement ∫\frac{1}{x^{2}*ln(x)} Homework Equations ∫udv = uv-∫vdu u=ln(x) du = \frac{1}{x}dx dv = x^{2}dx v = \frac{x^{3}}{3} The Attempt at a Solution Using the above formula I got \frac{x^{3}}{3}*ln(x) - \frac{x^{3}}{9} + C Am I doing this correctly or do I...

A friend posed this just for fun but now its really annoying me. how do you divide 90 into three parts so that each part is 1.6 times greater than the last. i.e: the second value should be 1.6 times greater than the first and the third value should be 1.6 times greater than the second? Im...

I understand this integration technique, for the most part. One thing I am curious to know is why, when you do your rudimentary substitution for this particular technique, does dv have to always include dx?

Homework Statement ∫ln(2x+1) Integrate by parts Homework Equations I got xln(2x+1)+\frac{1}2{}ln(2x+1)-x+C The Attempt at a Solution The solution is \frac{1}{2}(2x+1)ln(2x+1)-x+C I know the answers are the same,but it's bugging me that I can't simplify the first answer I got...

Homework Statement I have a general wave equation on the half line utt-c2uxx=0 u(x,0)=α(x) ut(x,0)=β(x) and the boundary condition; ut(0,t)=cηux where α is α extended as an odd function to the real line (and same for β) I have to find the d'alembert solution for x>=0; and show that in...

I have some problems understanding the intuition behind the integration by parts technique. I don't quite see why you solve for \int u(x)v\prime (x), instead of one of the other parts, what makes it easier to solve for that particular term? And in general when working with integration...

I know air conditioners use a significant amount of energy, but turning the fan on high uses a fairly negligible amount. This started me thinking about the engine of the car. Where do most of the losses occur? I know any time you have an energy conversion or transfer, you will be losing some...

Hello. I'm just trying to understanding something here. I was taught integration by parts by my professor in what looks to be like an untraditional way. From my understanding, the theorem states: ∫udv = uv - ∫vdu We were given an example in class of: ∫exsin(x)dx =∫ex∫sin(x)dx -...

I have no idea if I am picturing this whole scenario wrong, so please hear me out and try to point me in the right direction. Anyways, say we have a fast moving rocket with a person in it. Lightning strikes a side of it. So the light traveling from the bolt to the person/observer is traveling...

Other than the fan and hardrive, nothing else seems to be moving...

I would like to integrate by parts this term- \mu^2 (\nabla^2)^{-1} (\nabla\times B)\dot{B} Here B is a vector and \dot{B} is the time derivative of B. And \mu is just a constant. Can anyone help me?

Homework Statement The functional ##I(u,v)=\int_\Omega F(x,y,u,v,u_x,u_y, v_x,v_y)dxdy## The partial variation of a functional is given as ## \displaystyle \delta I =\int_\Omega (\frac{\partial F}{\partial u} \delta u+\frac{\partial F}{\partial u_x} \delta u_x+\frac{\partial...

FOlks, I am self studying a book and I have a question on 1)what the author means by the following comment "Integrating the second term in the last step to transfer differentiation from v to u" 2) Why does he perform integration by parts? I understand how but why? I can see that the...

Hi, I realize that this might be a silly question to ask without some proper background so: I'm a rising sophomore who is reviewing Calculus I-III right now. I first took Calculus as a junior in high school under the AP Calculus BC curriculum. I then took multivariate calculus and a semester of...

Homework Statement integral of e^-xsinxdx Homework Equations uv-/vdu The Attempt at a Solution u=e^-x du = -e^-xdx v=sinx dv=cosxdx e^-xsinx-/(-e^-x)sinx =e^-x(sinx+cosx) Wolfram alpha is telling me that the indefinite integral is actually "-1/2e^-x(sinx+cosx)" where did...

Homework Statement Integral, from 0 to 1, y/(e^2y) Homework Equations Use integration by partsThe Attempt at a Solution I need integration by parts. The answer is 1/4-3/5e^-2. But I got 1/2 and it all makes sense to me, so tell me what I got wrong. I put u=e^2y du=2e^2y dv= 1/e^2y dy (did...

Homework Statement Integral, from 4 to 6, 1/(t^2-9) dt Homework Equations please use my approach to solve it, like with cosh and whatnot The Attempt at a Solution Integral, from 4 to 6, 1/(t^2-9) dt so I multiplied the top and bottom by square root of 9. which got me...

Homework Statement In the section of the book of integration by parts, there is an exercise that I don't even know how to tackle anymore. It's this: \int \frac{xe^{2x}}{(1+2x)^2} dx Homework Equations {uv} - {\int v{du}} The Attempt at a Solution u = x ; du = 1...