Integrals Definition and 1000 Threads

Its been a while since I took calculus so I'm confused as how to solve this. I've gotten my equation simplified as far as BdT=KdP and I'm supposed to solve for dP I do it and end up with B(T2-T1) = K(P2-P1) but this is giving me the wrong answer when I put the values in... What...

Hi, I understand that from my EM class there exist a surface integral which is actually a way of summing infinitesimally small surface elements ds. But then I ran into some theorems on internet and I saw the denotation of double integral, over a surface S. And they called that a surface...

Homework Statement If we have volume integral of a Gaussian function, in phase space for example. F= \int^{\infty}_{-\infty} e^{-aq} d^{3}q Now, I think the the answer would be the standard answer for a Gaussian integral cubed wouldn't it? F=\left(\frac{\pi}{a}\right) ^{3/2} I...

Homework Statement A sleeve of mass m is constrained to move without friction along the x-axis. The sleeve is connected to the point (0, 2) on the y-axis by a spring as shown in the diagram below. Assume that Hooke’s “Law” is a good approximation for the restoring force exerted by the...

Homework Statement A cylindrical coffee cup (8 cm in diameter and 10 cm tall) is filled to the brim with coffee. Neglecting the weight of the cup, determine the torque at the handle (2 cm from edge of cup 5 cm up from bottom of cup). The easy way would be to just use the center of mass of the...

Hi all, can you help me to compute these integrals? \int \frac{x \sqrt{a x+b+x^2}}{d^2+x^2} \, dx \int \frac{x}{\left(d^2+x^2\right) \sqrt{a x+b+x^2}} \, dx a,b and d are real and positive. I tried with Mathematica, but the results involve logarithmic functions with complex...

Hi all, I have a family of functions defined by integrals and indexed by n, e.g f[x_,n_]=\int dy e^{ixy}y^n Is it possible to evaluate the integrals corresponding to different particular values of n in such a way that mathematica "remembers" that say f[x,4]= some function g[x]? An additional...

Homework Statement can anyone explain me about Integrals and derivatives in brief Homework Equations The Attempt at a Solution

Homework Statement There are two integrals that I don't know how to solve. I'm fairly certain the preceding work that led me to these integrals is correct. Homework Equations 1. ∫sin (x) / (csc (x) + cot (x)) 2. ∫x^(2) / (1 - x) The Attempt at a Solution U substitution didn't...

Homework Statement integral 1/x^(2/3)dx from -1 to 1 Homework Equations The Attempt at a Solution so i split it up into two integrals, one with limits going from -1 to b and the other with limits going from c to 1, and taking the limits as b and c go to 0 i know my antiderivative...

Homework Statement At my old university, Calculus was taught much differently than it is where I am now. My old school focused on numerical things, which this school focuses much more on pictures, abstract, etc. and it's very difficult for me. At my old school, we were given a shape...

Hi I have not studied calculus for a while and I am just seeking some clarification on the following two problems I have attempted to solve. PROBLEM 1 dy/dx = y(x^3 - √x) I have separated the variables as follows: Rewrote equation as dy/dx = y(x^3 - x^1/2) Divided both sides by...

Hi I have a little problem with the integrals of the following functions. integral from 0to 2pi ∫sin^2(nθ+ψ)dθ=∫cos^2(nθ+ψ)dθ=pi ψ=the phase angle.They occur in the theory of vibrations. Is it appropriate to set ψ=0 Thank you

Homework Statement \int cos^6(x) Homework Equations 1 = sin^2(x) + cos^2(x) The Attempt at a Solution \int cos(x) * cos^5(x) \int cos(x) * (cos^2(x))^3 \int cos(x) * (1-sin^2(x))^3 This is where I got lost, we just started this topic and I have a lot of homework to do...

The question asks to show using the residue theorem that \int cos(x)/(x2+1)2 dx = \pi/e (the terminals of the integral are -\infty to \infty but i didnt know the code to write that) I found the singularities at -i and +i so i think we can then say \intcos (z) / (z+i)2(z-i)2 dz...

If f is bounded on [a,b], can one define a Riemann-Stieltjes integral \int_a^b f(x) d\alpha(x) when the function \alpha(x) is not monotonically increasing on [a,b]? Rudin only seems to define R-S integrals with respect to monotonically increasing functions, but there are sources I've found...

Homework Statement \begin{equation} \int_{-1}^{1} e^{u+1} \end{equation} Homework Equations The Attempt at a Solution I really seem to struggle with any problems with e in them. I think I may have missed some of the basic rules or something, but I can't seem to find what I missed...

Homework Statement I=\int_{-\infty}^{\infty} { dx \over {5x^2+6x+5}}Homework Equations The residue theorem.The Attempt at a Solution I can't use the residue theorem since the denominator has real zeros. How should I solve this?

Hi, I saw a proof/argument done today that I think was wrong: It is finding the limit as a->oo of the integral from 0 to b<oo: Int_(0..b) Sqr[x(1 +cos(ax))]dx , where Sqr is the square root Now, the argument given was that one could find a bound for the oscillation of...

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...

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...