Double integral Definition and 558 Threads

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{...

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...

Hi, I'm having trouble understanding the solution to a question from my book. I think it's got something to do with the chain rule. The problem is to prove the change of variables formula for a double integral for the case f(x,y) = 1 using Green's theorem. \int\limits_{}^{} {\int\limits_R^{}...

Hi, I'm having trouble evaluating the following integral. \int\limits_{}^{} {\int\limits_R^{} {\cos \left( {\frac{{y - x}}{{y + x}}} \right)} } dA Where R is the trapezoidal region with vertices (1,0), (2,0), (0,2) and (0,1). I a drew a diagram and found that R is the region bounded...

I need to solve a double integral and I have no idea what to change the variables to: \iint_{R} \cos ( \frac{y-x}{y+x}) \ dA R=\{(x,y) \mid \ -x+1 \leq y \leq -x+2, 1 \leq x \leq 2 \} I tried to set u=y-x and v=y+x, but I still can't solve the resulting integral. I also tried setting...

Double integral of y^3, where D is the triangular region with vertices (0,0), (1,2), and (0,3). I can't figure out what the limits are. D={(x,y)|0<=x<=3...is this even half way right?

i have to setup a doble integral to find the volume of the solid bounded by the graphs of the equation. x^2+z^2=1, and y^2+z^2=1 z=sqrt(1-x^2) z=sqrt(1-y^2) then substituting in z=sqrt(1-y^2) into x^2+z^2=1, i got y=x. so when i setup a double integral for the dy i get integral...

i would need help with this integral: \int_a^{\infty}\int_a^{\infty}dxdyF(y/x) now i make the change of variable y/x=u x=v then what would be the new integration limits?..thanks. where a can be 0 or 1

Just had an exam and I had to evaluate the following double integral, with limited success :mad: \int_0^1 \int_0^{\pi} y\sin(xy) {dy} {dx} I managed to compute the first integral, that was ok, using parts. But trying to integrate that with respect to dx just yielded a whole lot of...

Greetings all, I need help setting up this problem: Use a double integral to find the area of the region enclosed by the curve r=4+3 cos (theta) Thanks

More fun yaaay evaluate \int \int \int_{G} x^2 yz dx dy dz where G is bounded by plane z=0, z=x, y=1, y=x certrainly zi s bounded below by 0 and above by x. and y is boundedbelow by 1 and above by x. having a hard time picturing this... i don't think this would pictured how the double...

*This was accidently posted in the 'Calculus & Analysis' section. Moderators can delete that one. Sorry.* I took a test today. I wanted to know if I set my limits up correctly and got the right answer, because I've been having problems with that. Okay, here is the question: A space is...

I took a test today. I wanted to know if I set my limits up correctly and got the right answer, because I've been having problems with that. Okay, here is the question: A space is bounded by x = 0, y = 0, xy-plane, and the plane: 3x + 2y + z = 6. Find the volume using a double integral...

Please help. Thank you.

problem: find volume bordered by cylinder x^2 + y^2 = 4 and y+z=4 and z=4. the answer is said to be 16p. but I couldn't find it. I found it in double integral part.so it must be solved with double integral. I tried with Jacobian tranformation. nut still couldn't solve it. I was confused...

The question is Evaluate the double integral over the region R of the function f(x,y)=(x/y -y/x), where R is in the first quadrant, bounded by the curves xy=1, xy=3, x^2 -y^2 =1, x^2-y^2 =4. Now it seems that a substitution would be the best bet. What I've done is make u=xy, and v=x^2...

How do I interchange the integration bound for the function below (change to dx dy): Integral from 1/2 to 1, integral from x^3 to x [f(x,y)] dy dx ?

Plz help me integrating the integral below...I did it to a certain point and got stuck...here is the integral and what I did: 1) Integral form 0 to pi/2, integral from 0 to a*sin(2*theta), [ r ]dr dtheta Inner integral: Int from 0 to a*sin(2theta) [(r^2)/2] dr = [a^2 * (sin(2 theta))^2 ] / 2...