Integrals Definition and 1000 Threads

I know the way to do \int sinxcos is by u-substitution but why doesn't the following work? sin(2x) = 2sinxcosx \\ \frac{sin(2x)}{2}=sinxcosx \\ \int sinxcosx= \frac{1}{2} \int sin(2x) = -\frac{cos(2x)}{4}

I was testing for convergence of a series: ∑\frac{1}{n^2 -1} from n=3 to infinity I used the integral test, substituting n as 2sin(u) so here's the question: when using the trig substitution, I realized the upperbound, infinity, would fit inside the sine. Is it still possible to make...

Homework Statement Please let me know if this kind of posting of exact problems from a textbook isn't allowed; if that's the case I'll delete it immediately. From Boas's Mathematical Methods in the Physical Sciences, Third Edition: The Fresnel integrals, \int_0^u sin (u^2)\,du and...

I am working on this question: ∫ [(3+ lnx)^2 (2-ln x)] / (4x) dx My answer is: 18/4 [ 3 (ln x^2/2) + 4 (ln x^3/3) - ln x^4/4 ] + C But the answer from the solutions is (5/12) (3+ ln x)^3 - (1/16)(3+lnx)^4 + C Where did I mess up? ∫ [(3+ lnx)^2 (2-ln x)] / (4x) dx let u =ln x du/dx =...

I am dumfounded on how one would perform surface integrals in Fortran 90 over a platelet, or a rectangular box. I can do single and double integrals but I have no idea on how to do surface integrals Thanks in advance!

Homework Statement The actual problem is ∫sin2x/((sinx)4+(cosx)4) dx Homework Equations The Attempt at a Solution First wrote the expression as ∫\frac{2sin2x}{((sinx)^2+(cosx)^2)^2+((sinx)^2-(cosx)^2))^2 } dx then I changed the 2dx to d(2x)...

Evaluate the Integral. Just need someone to check my work. $$ \int sec^4y \, tan^4y$$ $$\tan^4y * sec^2y * sec^2y \, dx$$ $$tan^4y * (1 + tan^2y) * sec^2y$$ $$u = tany$$ $$du = sec^2y$$ $$\int u^4 * (1 + u^2) * du$$ $$\int u^4 + u^6 * du$$ $$\frac{u^5}{5} + \frac{u^7}{7} + C$$...

Evaluate the following integrals. a) $\int^1_0 x e^x dx$ So integrating by parts we get $u = x $ $vu = e^x dx$ $du = dx$ $ v = e^x$ $uv - \int vdu = x e^x - \int^1_0 e^x dx$ $$xe^x - e^x |^1_0 = 1$$ b) $$\int^1_0 x^2 e^x \, dx$$ Integrating by parts we get $$u = x^2 $$ $$ dv =...

O.K. , this question is inspired by a physics class I'm taking where we're working out the expectation values of wave functions, but I think the question really belongs in the math section. Thank you in advance for any help. Here goes nothing... We have a function ψ(x,y,z) = x e\sqrt{}x2 +...

Homework Statement So I did an entire antiderivative, and ended with this part: sec(x)tan(x) + ln|sec(x) + tan(x)| + C I have to do this with the lower bound of -pi/3 and 0. When I do it, I should be getting 2√3 + ln(2+√3) But, I'm getting (0+0)-(2*-√3 + ln(2-√3)) Which would...

I have a question about work integrals. I'm trying to reconcile using integrals to essentially multiply force by distance, but the fact that there appear to be multiple different types of problems that seem to be fundamentally different is making it difficult. Here are some example problems...

Homework Statement https://www.physicsforums.com/attachment.php?attachmentid=66269&stc=1&d=1391481187 The questions are on the link above. Homework Equations P = (y + 60)/10 depth (D) = y + 60 The Attempt at a Solution a) I set up the double integral: Force (F) = ∫(0 ->...

Stuck on this problem. Evaluate $$ \int \cos^{2}x \, \tan^{3}x \, dx$$ What I have so far: used the trig identity sin/cos = tan factored out a sin so I can have a even power. changed $$\sin^{2}x$$ to its identity = 1/2(1 - cos2x) combined like terms and canceled out the cos $$\int \cos^{2}x...

Hi all, Homework Statement I have got a system described by this lagrangian L(\varphi ,\psi ,\vartheta ,\dot\varphi ,\dot\psi ,\dot\vartheta )=\frac{1}{2}m(\dot\varphi^2 +\dot\psi^2 +\dot\vartheta^2 )+cos(\varphi ^2+\psi ^2). I have to find all system's integrals of motion. 2. The attempt...

Quick question. $$\int sin^{4}x dx$$ so I know: $$\frac{1}{2} \int 1 - 2cos2x + \frac{1}{2}(1 + cos4x)dx$$ So here I first brought out the 1/2 because it's a constant and it's nasty. so now I have $$\frac{1}{4} \int 1 - 2cos2x + 1 + cos4x dx$$ so...Just as I brought 1/2 out can I now...

How can I write proper language for these integrals in MatLab ? Your helps really appreciated. John Mark

Suppose that the rate that people are getting infected in an outbreak of a virus is given by y=200xe^-0.5x. How many people in total will get infected from this outbreak? So i know I'm doing it right but i keep getting a strange number… so i set up an integral of that function from 0 to...

Hey, not too sure about what function i would compare this integral from 1 to infinity of (3x^3 -2)/(x^6 +2) dx. I also have to show that it converges. Thanks!

I need to find a function f(x) such that \int_{-\infty}^{100+10n} (f(x)) dx = 1-0.1^n for n=1,2,3,4,5,6...∞. How would I go about this? It must be exponential in some way I'm guessing? This is not a homework problem. I don't just want the answer. I want guidance on this type of problem...

1. Homework Statement ∫∫S xz dS where S is the boundary region enclosed by the cylinder y2 + z2 = 9 and the planes x = 0 and x + y = 5. 2. Relevant equation∫∫Sf(x,y,z)dS = ∫∫Df(r(u,v)) * |ru χ rv|dA 3. The Attempt at a Solution I think I have broken this up into 3 surfaces. The...

When doing surface integrals of surfaces described parametrically, we use the area element dA = ndS = (rv x rw)dvdw Where dS is the surface area element and v and w are the parameters. I'm fine with the derivation of this (I think) but I don't understand why it's necessary to have n and dS...

Hellow! A simple question: if exist the fundamental theorem of calculus for line integrals not should exist too a fundamental theorem of calculus for surface integrals? I was searching about in google but I found nothing... What do you think? Such theorem make sense?

Homework Statement Evaluate the iterated integrals (switch the order of integration if necessary) I just need someone to check my work. My professor gave us this practice test to help study for our final but it isn't much use if I don't know if I'm doing it correctly. I've been working...

Homework Statement ∫^{4}_{0} ∫^{√(4y-y^{2})}_{0} (x2) dx dy The attempt at a solution I'm confused on how to convert the bounds into polar coordinates. I believe x2 just becomes r2cos2θ 0≤x≤√(4y-y2) 0≤y≤4 but i don't know how to convert the bounds

I am confused as to what we are obtaining when taking these contour integrals. I know that the close loop contour integral of a holomorphic function is 0. Is this analogous to the closed loop of integral of a conservative force which also gives 0? Also when I am integrating around a...

Inspired by this http://mathhelpboards.com/calculus-10/powers-polylogarithms-7998.html we look at the generalization $$L^m_n(p,q)=\int^1_0 \frac{\mathrm{Li}_p(x)^m\, \mathrm{Li}_q(x)^n}{x} \, dx $$ This is NOT a tutorial. Any comments, attempts or suggestions are always welcomed.

If instead of evaluating the above line integral in counter-clockwise direction, I evaluate it via the clockwise direction, would that change the answer? What if I evaluate ##C_1## and ##C_3## in the counter-clockwise direction, but I evaluate ##C_2## in the clockwise direction?

Homework Statement The plane z = 2 and the paraboloid z = 8 − 6x2 − 6y2 enclose a solid. Use polar coordinates to find the volume of this solid. Homework Equations ∫∫R f(x,y) dA = ∫βα∫ba f(rcosθ, rsinθ) r dr dθ The Attempt at a Solution z = 2, z = 8 − 6x2 − 6y2 Setting these two equal, we...

Homework Statement Use polar coordinates to find the volume of the given solid. Enclosed by the hyperboloid -x2 - y2 + z2 = 1 and the plane z = 2 Homework Equations r2 = x2 + y2, x = rcosθ, y = rsinθ ∫∫f(x,y)dA = ∫∫f(rcosθ,rsinθ)rdrdθ The Attempt at a Solution -x2 - y2 + 4...

Homework Statement Which of the following double integrals would correctly solve this problem? Homework Equations The Attempt at a Solution I obtained two sets of boundary conditions. Set 1: $$x=-\sqrt{4-y^2}\quad (for\quad x<0)\quad to\quad x=\sqrt{4-y^2}\quad...

Homework Statement Evaluate the integral as either a volume integral of a surface integral, whichever is easier. \iiint \nabla .F\,d\tau over the region x^2+y^2+z^2 \leq 25, where F=(x^2+y^2+z^2)(x*i+y*j+z*k) Homework Equations \iiint \nabla .F\,d\tau =\iint F.n\,d\sigma The...

Here are the questions: I have posted a link there to this thread so the OP can see my work.

"The" Classical Path, QM Path Integrals and Paths in Curved Spacetime Hey Guys! I've got an exciting question! It's been burning on my mind for years, but I think I can formulate it now. It's not so much a specific question, but rather a physical story which perhaps this thread can uncover...

Homework Statement Assume that f(x,y,z) is a continuous function. Let U be the region inside the cone z=√x^2+y^2 for 2≤x≤7. Set up the intregal ∫f(x,y,z)dV over U using cartesian, spherical, and cylindrical coordinates. Homework Equations CYLINDRICAL COORDINATES x=rcosθ y=rsinθ z=z...

This is a forum where we chat about calculus problems that people are wondering about. I would greatly appreciate it if people also help answer some integration problems that have been nagging me for a while. Like ∫sin(sin(x))dx. Thanks Guys.

Here are the questions: I have posted a link there to this thread so the OP can see my work.

Homework Statement The integral of f(x) from 0 to 1 is 3, and the integral of f(x) from 1 to 3 is -2. What is the integral of f(x) from -3 to 3? Homework Equations FTC. The Attempt at a Solution From the equations given I know: F(1) - F(0) = 3, and F(3) - F(1) = -2...

Can someone make sure I'm on the right track with this problem? I'm a little confused because I thought that when you make a substitution you update the limits and get better numbers to work with when you plug them in the function in the end...Yet, it seems like I almost got worse numbers to...

Homework Statement Consider a vector A = (2x-y)i + (yz^2)j + (y^2z)k. S is a flat surface area of a rectangle bounded by the lines x = +-1 and y = +-2 and C is its rectangular boundary in the x-y plane. Determine the line integral ∫A.dr and its surface integral ∫(∇xA).n dS Homework...

Homework Statement Consider a vector A = (x^2 - y^2)(i) + xyz(j) - (x + y + z)k and a cube bounded by the planes x = 0, x = 1, y = 0, y = 1, z = 0 and z = 1 Determine the volume integral ∫∇.A dV where V is the volume of the cube Determine the surface integral ∫A.n dS where s is the surface of...

On the bottom of page 24 & top of page 25 of this pdf an integral is beautifully computed by breaking it up into an infinite series. Is there any reference where I could get practice in working integrals like these?

EDIT: I left out something of major importance, I want to maximize with respect to a! Good day, I've run into an issue in solving a certain problem with matlab, and I was hoping if anyone could help me out. I am relatively new to matlab, so I don't even know if this is possible, but I...

EDIT: I left out something of major importance, I want to maximize with respect to a! Homework Statement My problem is rather complex, but in the end it boils down to maximizing the fraction Homework Equations With the calculus I know, I can't evaluate these integrals, so I have no applicable...

Homework Statement Rewrite the given sum of iterated integrals as a single iterated integral by reversing the order of integration, and evaluate. $$\int_0^1 \int_0^x sin x dy dx + \int_1^2 \int_0^{2 - x} sin x dy dx$$ Homework Equations None The Attempt at a Solution I drew the domains of...

Homework Statement This is just an example, not a specific problem. So if I have ∫σ(sinx), for example, and my limits of integration are, for example, 1 to 10, what I need to do to solve that is to find a value of x that would make the argument of the delta function 0. So for sinx, 0 makes...

Integrate the function f(x,y,z)=−7x+2y over the solid given by the "slice" of an ice-cream cone in the first octant bounded by the planes x=0 and y=sqrt(263/137)x and contained in a sphere centered at the origin with radius 25 and a cone opening upwards from the origin with top radius 20. I...

[1] $\displaystyle \int\sqrt{\frac{\csc x-\cot x}{\csc x+\cot x}}\cdot \frac{\sec x}{\sqrt{1+2\sec x}}dx$ [2] $\displaystyle \int \frac{3\cot 3x - \cot x}{\tan x-3 \tan 3x}dx$ Thanks pranav I have edited it.

I've recently been working on a number of integrals related to the loggamma function, so I thought I'd share my results here. I'll have to post as and when I have time, and there will be a fair bit of preliminary work before we get to the final results, but - loosely speaking - the main aim here...

Hi all, The context of this problem is as follows: I'm trying to implement a discontinuous finite element method and the formulation calls for the computation of line integrals over the edges of the mesh. Anyway, more generally, I need to evaluate \int_{e}f(x,y)ds, where e is a line segment...

Homework Statement A crate of mass 9.6 kg is pulled up a rough incline with an initial speed of 1.44 m/s. The pulling force is 92 N parallel to the incline, which makes an angle of 19.4° with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 4.92 m. (d)...