Integrals Definition and 1000 Threads

Homework Statement Knowing what I do (U-Substitution, beginning Integration by Parts) what would you do for these? (ln t)^2 (sin t)^2 Homework Equations The Attempt at a Solution All I have been able to do is change these to (ln t)(ln t) and then try by parts, but I just end...

When Logarithm are Defined as integral and the Exponetial functions are defined to be its inverses , then What can prove ? or why ? a^n = \underbrace{a.a.a...a}_{n-times} : n\in N also Why we define rational exponents as roots? I am sorry If my Question is silly. IS my Question...

I posted this in the aerospace engineering forum but I think it may get more replies here: I've been trying to compute the bending-torsion coupling constants for a wing, B1, B2 and B3. The expression for this is \begin{bmatrix} B_1 \\ B_2 \\ B_3 \end{bmatrix} = \iint (y^2 +...

I've been trying to compute the bending-torsion coupling constants for a wing, B1, B2 and B3. The expression for this is \begin{bmatrix} B_1 \\ B_2 \\ B_3 \end{bmatrix} = \iint (y^2 + z^2)\begin{bmatrix} y^2 + z^2 \\ z \\ y \end{bmatrix}dydyz where x is in along the wingspan direction, y...

Hi, if you have the book: Physics for Scientists and Engineers 8E, Serway Jewett On page 675 (Chapter 23), Example 23.8 there is a step taken during the integration I don't understand: How do you go from "2r dr" in the numerator to d(r^2)? If there is info or link to the property of...

\mathop\int\limits_{\infty} \log[(z-1)(z+1)]dz=A(z)\biggr|_0^0=4\pi i The infinity symbol below the integral is a positive-oriented, closed, and differentiable path over the function looping around both branch-points and A(z) is the antiderivative of the integrand. I mean would that hold for...

Hello, I tried to read Feynman's book: Quantum Mechanics and Path Integrals but it is so difficult. Is it a really important book if you want to learn Quantum Mechanics? If so what should I do in preparation to read it? Thanks

It is frequently stated that path integral formulation of quantum mechanics is equivalent to the more traditional canonical quantization. However, I don't think it is really true. I claim that, unlike canonical quantization, path integral quantization is not self-sufficient. That's because...

I'm a new Calculus student, and it's killing me! Please help! :( Thank you Homework Statement Find to 2-decimal place of the following integrals. Homework Equations 1. (Upper limit= 33, lower limit= 18) 1 / ([7x+8]^0.25) dx 2. (Upper limit = 33, lower limit = 5) (x^1.6 + 26)...

Homework Statement ∫(from pi/4 to pi/2)sin x/x ≤ 1/√2. Homework Equations The Attempt at a Solution I know the pi/4≤x≤pi/2 and so 1/√2 ≤ sin x ≤ 1 and i have tried to manipulate this to no end and it has annoyed the living daylights out of me

hello all! I just got a new computer with an Nvidia card, and am now able to do some GPU parallel processing inside mathematica using CUDA. My main interest is in taking tons of moderate accuracy (3-4 digits) numerical integrals. I've been using QMC in MMA and that's been working well...

in line integrals we always need a vector element of distance. I can't understand the difference between ds and dr. is ds for all kinds of paths (even curly ones) and dr only for straight lines, or theyre the same? I am confused, or maybe dr is just the magnitude of ds, and the vector here is...

I'm confused as to when to change the limits on a definite integral. Ex. Integral with the limits a=1, b=5, 3/(x+1)dx I set u = x+1 and du = dx I used u-substitution and everything worked out fine. However for this one... Ex. Integral with the limits a = 0, b = 2...

Hi, I was wondering if it was really necessary to evaluate improper integrals with limits? Could anyone really say I was wrong if I did something like find the area bounded by the region y=1/x^2, x=2, and the x-axis integral[1,inf] dx/x^2 = (-1/x)|[2,inf] = (-0)-(-1/2)=1/2 Like I don't...

Let's say we have the statement \sum^{\infty}_{0}f(x)=\frac{\sum^{\infty}_{0}g(x)}{\sum^{\infty}_{0}h(x)} does this imply that \int^{\infty}_{0}f(x)=\frac{\int^{\infty}_{0}g(x)}{\int^{\infty}_{0}h(x)}? Also if \sum^{\infty}_{0}f(x)=\sum^{\infty}_{0}g(x) does this imply that f(x)=g(x), or...

Hey, I was just going through my vector calc textbook for this year and everything was going well until I reached double and triple integrals. My problem is the whole symmetry thing; when does (forgive me, I can't figure out the symbols) the integral from a to b become twice the integral from...

Homework Statement Suppose s'(t) is a velocity function, then which of the integral will give you the total distance? (1) \int_{a}^{b} \sqrt{1 + [s'(t)]^2} dt (2) \int_{a}^{b} |s(t)| dt The Attempt at a Solution No clue at all... the first is arc length, so it is like...

1. Find the volume, using triple integrals, of the region in the first octant beneath the plane 2x+3y+2z = 6 2. http://tutorial.math.lamar.edu/Classes/CalcIII/TripleIntegrals.aspx SOLUTION: 1. Assume X and Y are 0. Solve for Z: 2(0)+3(0)+2z=6 => z=3 (0,0,3) 2. Assume X...

Hi, I wanted to calculate elliptic integrals (K & E) for a given function in Mathcad. I was not able to find the appropriate function. I am using Mathcad 15. Regards, -sgsawant

The problem is: R is the parallelogram bounded by the lines x+y=2, x+y=4, 2x-y=1, and 2x-y=4. Use the transformation u=x+y and v=2x-y to find the area of R. I am not sure how to complete this problem. My first issue is that I don't know how to convert the transformation functions into...

Homework Statement solve the integral [abs(x+1)(3+abs(x))]/(x+1) between -3 and 1 Homework Equations The Attempt at a Solution when x<-1 then [abs(x+1)(3+abs(x))]/(x+1) = [-(x+1)(3-x)]/(x+1) = -(3-x) when -1<x<0 then [abs(x+1)(3+abs(x))]/(x+1) = (x+1)(3-x)/(x+1) = 3-x when x>0...

Homework Statement Hi, I'm trying to solve this problem and guess I'm doing something wrong. Evaluate Integral tan(x)^5*sec(x)^4 dx Homework Equations integral tan(x) dx = ln(|sec(x)|) integral tan(x)^n dx = tan(x)^(n-1)/(n-1) - integral tan(x)^(n-1) dx tan(x)^2+1=sec(x)^2 The Attempt at...

Hi, I just had this idea pop into my head... Can you use a trig sub with a reference triangle who has sides equal to zero? or more like a value close to zero such as dx or da or something? For example integral 1/sqrt(9+dx^2) (dx)^2 would have a reference triangle were the hypotenuse is...

Homework Statement Evaluate integral csc(x)^4/cot(x)^2 dx Homework Equations The Attempt at a Solution Apparently I'm doing something wrong, what I'm not sure, thanks for any help My Answer: 2*tan(x) - (sec(x)^2*tan(x))/3 + c integral csc(x)^4/cot(x)^2 dx used fact that...

Homework Statement Evaluate integral sin^(-3/2)(x)cos^3(x) dx Homework Equations tan(x)=sin(x)/cos(x) sin^2(x)+cos^2(x)=1 sin^2(x)=(1-cos(x))/2 cos^2(x)=(1+cos(2x))/2 integral cos(x)dx = sin(x) + c integral sin(x)dx = -cos(x) + c d/dx sin(x) = cos(x) d/dx cos(x) = -sin(x) a^m/a^n=a^(m-n)...

Homework Statement Hey people got a question here about complex integration, not really sure how to do it so hope someone out there could help me! Evaluate the complex integrals ∫ c { (zbar)^2 +1 } dz...and...∫ c { zcos(z^2) - ie^2z } where c is the contour joining 0 to 2i along...

Homework Statement Evaluate integral( sin^3(x) cos^5(x) ) dxHomework Equations sin^2(x) + cos^2(x) = 1 integral x^n dx = x^(n+1)/(n+1) + c d/dx cos(x) = -sin(x) a^n*a^m=a^(n+m) The Attempt at a Solution I got -cos^6(x)/6+cos^8(x)/8+c Apparently I did something wrong SEE ATTACHMENT Thank...

Homework Statement Apparently I'm doing something wrong. I'm kind of lost as to what because I looked over my work several times. Homework Equations sin^2 x = ( 1 - cos 2x )/2 cos^2 x = ( 1 - sin 2x )/2 integral sin(x) dx = -cos(x) integral cos(x) dx = sin(x) The Attempt at a...

Homework Statement I (came up with)/(heard about) a way of using Laplace transforms that I didn't think about before. The problem is that it doesn't work for some reason. Look at following integral: I = \int_{0}^{\infty }sin(t)dt Say that you had no idea how to integrate something...

Homework Statement ∫ |x^2 -9| [0-4] Homework Equations The book answer states the same EXCEPT splits into [0-3] and [3-4]. Other problems split the integral perfectly in half for absolute values...why would it differ and are there rules to figure this out? Larson's Calculus has no...

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...

Hello everyone. In Mathematica® I want to numerically integrate a function of k variables (k varies) with respect to all of them. Does anyone of you know a way to do that? I tried the following simplified example. k = 5; int[x_] := x[[1]] + x[[2]] + x[[3]] + x[[4]] + x[[5]] ; (* My...

This isn't homework. I've been restudying vector calculus from the beginning to end on my free time and got stuck on this problem. I am not sure what I'm doing wrong, but it may be a calculation error since it has so much calculation involved. Homework Statement Evaluate the surface integral...

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...

Homework Statement Homework Equations The Attempt at a Solution Why I can't integrate\theta from 0 to 2\pi? Then integrate \varphi from 0 to \pi. It seems it can also generate a sphere.

Homework Statement I have a problem in part b Homework Equations The Attempt at a Solution How to integral the function?

I've been solving this exercise and I came to a point when one function can get two different integrals: Am I doing something wrong? Because both functions are the same, and the integrals (indefinite) are really different. This is a huge problem, because this is almost the final step of an...

Suppose I know the value of an integral: \int_0^T cos(\theta)dt = x Is there any way to evaluate the integral \int_0^T sin(\theta)dt solely from this information? EDIT: \theta=\theta(t), i.e. \theta is a function of t.

This is a continuum mechanics/fluid dynamics question concerning the time rate of change of a surface integral of a vector field, where the surface is flowing along in a velocity field (like in a fluid). (Gauss's law is for fixed surfaces.) This integral goes by various names in different...

Homework Statement \int (x+1)^2 dx Homework Equations The Attempt at a Solution I am just getting into this, and this is a simple problem, but my book and I took two separate routes. My question, essentially, is does any constant you get just "combine" with the "any constant" C...

Write a triple integral to represent the volume of the solid The wedge in the first octant and from the cylinder y^2 + z^2 <= 1 by the planes y=x, x=0, z=0 First.. i find the range for z..; 0 <=z<= sqrt(1- y^2) then... i find the range for y..; let z =0 0<=y<=1 next, if i...

What class will I start to study these?

Homework Statement Homework Equations The Attempt at a Solution I don't understand what exactly is going on here. They let u=(1+x^{2}), so that leaves them with this: \int \frac{x}{u^{2}}dx The derivative of (1+x^{2}) is simply 2x. And so: \frac{du}{dx} = 2x \rightarrow du =...

Hey there.. i try to solve the question below.. but.. i still didn't get the answer given by my lecturer.. the answer should be.. pi/4(e - 1) where did i do wrong? http://imageshack.us/photo/my-images/215/06072011697.jpg/ http://imageshack.us/photo/my-images/17/06072011699.jpg/...

hello,everyone i want to know how to solve this bessel function integrals: \int_{0}^{R} J_m-1(ax)*J_m+1 (ax)*x dx where J_m-1 and J_m+1 is the Bessel function of first kind, and a is a constant. thanks.

Homework Statement The Gamma and Beta integrals are defined respectively as \Gamma (z) = \int^{\infty}_0 t^{z-1} e^{-t}\;dt B(p,q) = \int^1_0 t^{p-1} (1-t)^{q-1}\;dt. Determine for what values of the complex parameters z, p, q the integrals converge absolutely and explain why. The...

I am just starting to do double integrals and came acorss an issue. I remembered from single integrals when we integrate from limits for say -1 to 1, we can double it and change integration limits to 0 to 1. Now, when is this the case? Basically, when can we not do this?

I'm integrating 1/(z-1/2) over the closed disk w/ radius = 3 centered at 0. I've seen other problems where the final answer was i2pi times f(w) - here w =1/2. Since f(z) is equal to 1. Is the final answer just i2pi? Next up: I have the integral of dt/(2 + sint) the problem then tells me...

Homework Statement In an effort to keep me from spending all summer lying on the couch, I recently started reading Michael Spivak's Calculus on Manifolds; while working on problem 1-6 I got stuck on a technical detail and I was wondering if anyone could provide a little insight. Problem 1-6...

Homework Statement I've come across integrals of exponential and trig functions and I have no idea how to do them. Integration by parts doesn't really work because they just derive into either e or another trig function. One of them is \intsin(a)*sin(b - a)da Another is \inte(a)*sin(a)da...