Double integral Definition and 574 Threads

desperate college student needs help in double integral! here is the problem I couldn't solve, anyone got any idea please help me. thank you very much in advance 1) use double integrals to derive the given formula for the volume of a right circular cone of radius R and height H. the volume of...

[SOLVED] Need Help With a Double Integral Any help on the following integral would be appreciated. I don't know where to begin at all. \int_0^{1}\int_{arcsiny}^{\pi/2} sec^2(cosx) dxdy I've thought about changing the order of integration, but I don't think that will...

Homework Statement Evaluate the integral \int {\int\limits_R {\left( {x + y} \right)\,dA} } where R is the region that lies to the left of the y-axis between the circles x^2 + y^2 = 1 and x^2 + y^2 = 4 by changing to polar coordinates. Homework Equations x=r cos theta y=r sin...

Homework Statement Let D be the region given as the set of (x,y) where 1 <! x^2+y^2 <! 2 and y !<0. Is D an elementary region? Evaluate \int\int_{D} f(x,y) dA where f(x,y) = 1+xy. Homework Equations The Attempt at a Solution So I understand that this is two concentric circles(an...

I'm having trouble trying to setup this double integral. The question asks to find the volume of a solid enclosed by the parabolic cylinder y = x^{2} and the planes z = 3y, z = 2+y I'm not even sure where to start. I have drawn the figure and understand that you have to integrate the two...

[SOLVED] Double integral with cos(x^n) term Homework Statement Solve the following integral (without using a series development): \displaystyle \int _{0}^{\frac{1}{8}}\int _{\sqrt[3]{y}}^{\frac{1}{2}}\cos\left(20{\pi}x}} ^{4}\right)dx dy Homework Equations N/A The Attempt at a...

Homework Statement Evaluate \int\int e^x^2 dx dy. The bounds for the inner integral go from y to 1 The bounds for the outer integral go from 0 to 1 2. The attempt at a solution I can easily do this, I just do not see how I can get e^x^2 to integrate for x. Is there some sort of special...

I can do this problem if they give a general equation, but the infinite boundaries are confusing me. I don't know how to inert all the symbols so I'll link you to the problem. It's problem number 105 in the packet. http://www.math.ufl.edu/%7Ehuang/calc3/fall2007.pdf

Homework Statement Evaluate: \int_{0}^{4} \int_{\sqrt{x}}^{2}e^y^3dxdy The Attempt at a Solution Well that's a Fresnel type function so you can't find an antiderivative for it. I'm pretty sure the point of this assignment isn't Taylor series so I'm quite certain we aren't...

I'm supposed to prove that \int\int_{S}^{}\ f(ax + by + c) \, dA \ =2 \int_{-1}^{1} \sqrt{1 - u^2} f(u\sqrt{a^2 + b^2} + c) \, du Where S is the disk x^2 + y^2 <= 1. It is also given that a^2 + b^2 is not zero I can´t use polar coordinates and I can´t see how you simplify the surface S...

The function F(x,y) = 4x^2y^3 over the disk x^2 + y^2 =1 is supposed to be zero over the disk. I'm wondering how you can see it? I cannot see this or imagine it in 3D. Is it because the function is odd in terms of y? F(x,-y) = -F(x,y) ? independent of wheher x is positive or negative...

Homework Statement Using transforms: u = 3x + 2y and v = x+4y solve: \iint_\textrm{R}(3x^2 + 14xy +8y^2)\,dx\,dy For the region R in the first quadrant bounded by the lines: y = -(3/2)x +1 y = -(3/2)x +3 y = -(1/2)x y = -(1/2)x +1 I'm itching to see where I've gone wrong on this one...

[SOLVED] Absolute Value in a double integral Homework Statement If \Omega = [-1,1] x [0,2], evaluate the double integral \int\int_{\Omega} \sqrt{|y-x^{2}|} dA given that it exists. Homework Equations None The Attempt at a Solution I know that in order to integrate with the...

Okay I have no idea where to start on this example problem: Use polar coordinates to evaulate the double integral e^((x^2)+(y^2))dydx [frist (inner) integal lower limit y= -sqrt(4-x^2) upper limit y=0)] [second (outer) lower limit x=0 upper limit x=2] When I start doing the integral...

Hi, I am having some difficulties integrating the following expression.. \int\int\left(\frac{k}{\pi}\right)^2 \frac{1}{k^2+\omega'^2}\frac{1}{k^2+\omega^2}e^{-i\omega'\tau}e^{i\omega\tau}d\omega d\omega' I've tried by part but it doesn't look like it's going to give me the right answer...

Double integral question... Homework Statement Evaluate the integrals shown ( I have attached the file with the integral). Homework Equations The Attempt at a Solution Ok, for the first one, can you tell me how I integrate sin x^2...?? which method should i use? And for the...

Homework Statement Evaluate the integral shown ( I have the file with the given integral attached here). Homework Equations The Attempt at a Solution So what i did was change dy dx into dx dy. Then i integrated y so the whole thing becomes 2x - y^3. I plugged the values (1+x)...

1. Integrate f(x,y)=x+y 1<=x^2+y^2<=4, x>=0, y>=0 3. ∬x+y dxdy x=rcos(o) y=rsin(o) ∬r(rcos(o)+rsin(o))drdo r is from 1 to 4, o is from 0 to pi/2 I get the wrong answer and don't know why

hello i have this problem about polar form, i am aware that when you have a problem like \int\int x^2 + y^2 dxdy you use r^2 = x^2 + y^2 but i what would you do if you had a problem like \int\int xy dxdy? thanks in advance. edit: i know the limits if you need them please let me know but i...

double integral of xy dA in the triangular region of (0,0), (3,0), (0,1). my problem that I am having is finding the limits I am suposed to find dx or dy in. I figure I should use 0 to 3 for dx, but then i do dy from 0 to what? Help appreciated.

Homework Statement Evaluate the integral shown in the diagram Homework Equations The Attempt at a Solution The first step to evaluating the integral is shown in the diagram (labelled as 2). They said they changed the order of integration. I was wondering what they mean by...

Find the mass of a right circular cone of base radius r and height h given that the density varies directly with the distance from the vertex does this mean that density function = K sqrt (x^2 + y^2 + z^2) ? is it a triple integral problem?

Evaluate the volume of the solid bounded by the plane z=x and the paraboloid z = x^2 + y^2 I have tried to graph this, and they don't bound anything? have i graphed it wrong. and is there a way to do these problems where you don't need to draw the graph.

I am trying to work through some examples we have been given on flux out of a cube but am having difficulty in seeing how one one line of the answer becomes the next. The question is analysing the flux out of a cube by looking at each side individually and working out the surface integrals...

Basically I want to find the new limits w,x,y,z when we make the valid transformation \int^{\infty}_0 \int^{\infty}_0 f(t_1,t_2) dt_1 dt_2 = \int^w_x \int^y_z f(st, s(1-t)) s dt ds I've tried putting in arbitrary functions f, and so getting 4 equations constraining the limits, but I end up...

Show that if f is defined on a rectangle R and double integral of f on R exists, then f is necessarily bounded on R.

If we wish to calculate the integral. \int_{0}^{\infty}dx \int_{0}^{\infty}dy e^{i(x^{2}-y^{2}} which under the symmetry (x,y) \rightarrow (y,x) it gives you the complex conjugate counterpart. my idea is to make the substitution (as an analogy of Laplace method) x=rcosh(u) ...

doubleIntegral( |cos(x+y)| dx dy ) over the rectangle [0, pi]x[0,pi] I tried several ways to split the integral up so that I could remove the absolute value sign and integrate. However, I did not get the correct answer, so I must be splitting it wrong. Can someone show me how to split the...

For the double integral find which values of k make it converge. \int \int \frac{dA}{(x ^ 2+y^2)^k} x^2 + y^2 <= 1 I have no idea how to even start going about this, can just about do the basics of multiple integration but not this.

From an example in my book: Int Int (2x) dxdy over R = 0 (R is the circe x^2+(y-1)^2=1) How can one make this conclusion without integrating?

Int Int (x*y^3 + 1) dS where S is the surface r=1, tetha from 0 to Pi and z from 0 to 2. How can I solve this integral? I haven't got a clue.

Evaluate. double integral (e^(y^3)) dy dx Where dy is evaluated from sqrt(x/3) to 1 ...and dx is evaluated from 0 to 3. I am lost. I don't even know how to start.:frown:

Please help me with folllowing double integral \int\limits_{ - \infty }^\infty {\int\limits_{ - \infty }^\infty {e^{ixy} dxdy = 2\pi}} (x,y, real) It came out analyzing the relation between DiracDelta and the Fourier Transform formula. (it's the reason why insert the constant...

It's about finding the area of the paraboloid z=x²+y² beneath z=2. The area integral is \int\int_{\{(u,v): u^2+v^2<2\}}\sqrt{1+4(u^2+v^2)}dudv A polar change of variable seems to fits nicely: =\int_0^{\sqrt{2}}\int_0^{2\pi}\sqrt{1+4r^2}rd\theta dr Then the change of variable \xi=1+4r^2...

1.Set up the integral to Find the volume enclosed by the cylinder x^2 +y^2 = 1 x=0 and z=y 3. The area to integrate over is the part of x^2 + y^2 =1 above the x axis. X goes from -1 to 1 and y goes from 0 to sqrt(1-x^2) So the integral should be: \int^1_{-1} \int^{\sqrt(1-x^2)}_0 y dy dx

Hey everyone, My task this time is to derive the volume of a sphere using a polar double integral. The sphere has radius a we know that r goes from 0 to a in this integral. The equation for a sphere is: x^2 + y^2 +z^2 = r^2 or f(x,y) = \sqrt{r^2 -x^2 -y^2} and it intersects the x-y plane...

Here is the problem: http://img141.imageshack.us/img141/3830/problemsm5.jpg Is it possible to determine this moment of inertia in this problem using double integrals of the form: http://img172.imageshack.us/img172/1219/momented0.jpg I could do this problem using double integrals if the...

I'm having trouble finding the function and/or the limits to this problem: Using polar coordinates, evaluate the integral http://ada.math.uga.edu/webwork2_files/tmp/equations/01/19aeef09224e0fca11ef9d6e45fb311.png where R is the region...

Here's the question: We want to evaluate the improper integral http://ada.math.uga.edu/webwork2_files/tmp/equations/6c/4073055a5b909be16e2abc5bd3dfc61.png Do it by rewriting the numerator of the integrand as...

hi how r u all i have a small problem with this proof i want the solution without using double integral that `s the proof http://s07.picshome.com/ce2/aaa.jpg

given \phi to be a function of x and t, how do you solve 2\int_{0}^{\infty}\int_{x}^{\infty}\frac{\partial^{2}\partial\phi}{\partial t^{2}} dt dx - 2\int_{0}^{\infty}\int_{0}^{t}\frac{\partial^{2}\partial\phi}{\partial x^{2}} dx dt any hints would be great. thanks!

double integral (6x^2 -40y)dA where it is a trianglewith vertices (0,3) , (1,1) and (5,3) may i know how to divide the region according to this triangle??

Question: At airports, departure gates are often lined up in a terminal like points along a line. If you arrive at one gate and proceed to another gate for a connecting flight, what proportion of the length of the terminal will you have to walk, on average? One way to model this situation is...

I am having trouble with this seemingly easy problem. Evaluate the double integral (sin(x^2+y^2)) , where the region is 16=<x^2+y^2=<81. I find the region in polar coordinates to be 4=<r=<9 0=<theta=<2pi I find the expression to be sin(rcos^2theta+rsin^2theta) r dr dtheta , which is...

\int _0 ^{\pi/3} \int _0 ^{\pi/4} x cos(x+y) dy dx \int _0 ^{\pi/3} xsin(x+\frac{\pi}{4}) dx using u-sub, u=x, dv=sin(x+pi/4) -xcos\left(x+\frac{\pi}{4}\right)+ sin\left(x+\frac{\pi}{4}\right)-sin\left(\frac{\pi}{4}\left) |_0^{\pi/3}...

i have the integral \int_{0}^{\infty} \int_{0}^{\infty} (-x^2-y^2) \ dx dy (double integral with both limits the same...assuming my first bash at the tex comes out it says to transfer it into polar form and evaluate it i have no idea how to convert a limit of infinity to polar form, help...

Hi, I am new here, but apparently there are some decent mathematicians around, so I would like to confront you with a double integral problem. Consider \psi_n(z) = \int_0^{2\pi}\int_0^1 \frac{ (z-\frac{1}{2}) \cdot (r \cos(\theta) + \frac{1}{2})^n \cdot r} { \sqrt{...

given f(x,y) = x-y R is a triangle with vertices (2,9), (2,1), (-2,1) then i need to find I, I = int. int. (x-y) dx dy i was taught to use this range when i do the dbl. integration 1 <= y <= 9 (y-5)/2 <= x <= 2 i want to ask, why can't i use this range: 1 <= y <= 9 -2...

I was fine with these in class, tutorials etc. It's only since I found this in a past paper that I've had a problem with them. \[ \int_0^1\! \int_{\sqrt{y}}^1 9\sqrt{1-x^3}\,dxdy.\] Nomatter what I substitute in under the sqrt sign I just can't get out the integral for x :( I tried...

Anybody know how to integrate over... Z^2 = 4x^2 + y^2 with the plane z = 1 ? this comes from my class notes... hmmm.. the proff did some thing really messy... or at least i wrote it messy... but i got 0(integral)2pi 0(integral)1 z dz d(pheta) which doesn't seem to make...