Double integral Definition and 558 Threads

My problem: I don't know how to begin with this problem.

Homework Statement Use polar coordinates to set up and evaluate the double integral f(x,y) = e-(x2+y2)/2 R: x2+y2≤25, x≥0 The Attempt at a Solution First I just want to make sure I'm understanding this my double integral would be ∫^{\pi/2}_{-\pi/2} because x≥0 ∫^{5}_{0}...

Homework Statement Evaluate the following integral with a change of variable of your choice. \int_0^{1} \int_y^{y+2} \sqrt{(x-y)}dxdy The Attempt at a Solution I'm supposed to choose a u and v that will simplify the integral, but I have no idea how to even start this. I tried...

so in the image in the link below, i don't understand a couple of things: 1.) the center of the cylinder is off to the side and not at the center. where/how in the problem are we taking this into account? because it should definitely affect the volume under the parabaloid right? 2.) most of...

Homework Statement Set up a double integral to find the volume of the solid bounded by the graphs y=4-x2 and z=4-x2 The attempt at a solution I drew myself a 3d graph but it's just a parabloid in the xy plane and a parabloid in the xz plane right? so I'm unsure how to set up my...

$$f(x,y)= \begin{cases} 4(x+y^2),&\text{if x > 0, y > 0, x + y < 1} \\ 0, &\text{elsewhere} \\ \end{cases}$$ Find two different integral expressions for P(y > x) (1) $$\int_{0} ^{1/2}\int_{0} ^y 4(x+y^2),dx\,dy + \int_{1/2} ^{1}\int_{0} ^{1-y} 4(x+y^2),dx\,dy $$ (2) $$\int_{0} ^{1/2}\int_{x}...

Homework Statement Determining two sets of boundary conditions for a double integral problem in the polar coordinate system. Is the below correct? Homework Equations The Attempt at a Solution There are two sets of boundary conditions that you can use to solve this problem in the polar...

Homework Statement http://i.imgur.com/d4ViHux.png Homework Equations The Attempt at a Solution The author writes: "Now, using symmetry, we have..." But what symmetry does the author use? Also, I got the integral as shown in the remark but why is it wrong?

is there a closed form solution for this double integral? \int^{2}_{1}\int^{3}_{4}\sqrt{1+4x^{2}+4y^{2}}dydx

Here is the beast \iint_{(ax+\mu _{1})^{2}+(bx+cy+\mu _{2})^{2}\leqslant z}\frac{1}{2\pi \sigma ^{2}}e^{-(\frac{1}{2\sigma ^{2}})(x^{2}+y^{2})}dxdy The integral gives the C.D.F. of (ax+\mu _{1})^{2}+(bx+cy+\mu _{2})^{2}\leqslant z where x and y are identically distributed gaussian random...

Homework Statement The problem states: Use cylindrical coordinates to evaluate \iiint_V \sqrt{x^2 +y^2 +z^2} \,dx\,dy\,dz where V is the region bounded by the plane z = 3 and the cone z = \sqrt{x^2 + y^2} Homework Equations x = r cos( \theta ) y = r sin( \theta ) z =...

Homework Statement Double Integral Surface Area of Spherical Ball radius Homework Equations ##\int_S d\vec{S} = 4*\pi*a^2## The Attempt at a Solution ##\int\int_0^a f(r,?) dr d? = 4*\pi*a^2##

1. Evaluate the double integral ∫∫arctan(y/x) dA by converting to polar coordinates over the Region R= { (x,y) | 1≤x^2+y^2≤4 , 0≤y≤x } My attempt at solving Converting to polar using x=rcosθ and y=rsinθ I get ∫∫arctan(tan(θ))r drdθ I understand that I have to integrate first with respect...

Homework Statement ∫∫x^4ydxdy x [-5,10] y [-1,1] (don't know how to do a definite integral in the math code...) The answer choices are A)10^5 B)0 C)-10^{10} The attempt at a solution \frac{x^5y}{5} evaluated at -5 to 10. then ∫20625ydy evaluated at -1 to 1. My final answer is 20625. What...

Homework Statement Evaluate the double integral of (2+xy^2) over dA (dxdy) using symmetry where R = [0,1] x [-1,1] Homework Equations The Attempt at a Solution I don't know how to use symmetry to evaluate this.. However if I integrate this integral normally i first get...

Hi! Need help in solving this double integral: 1 1 ∫ ∫ |x-y| dydx 0 0 Thanks in anticipation. Regards, Aby.

"Hey guys, how are you? I was studying for my calculus final and stumbled upon a peculiar function. Homework Statement Now I have to find the area bounded by the function (x^2+y^2)^3=xy^4 using a double integral. Now, the problem is that the graph is totally unknown to me (I have some...

Hey guys, how are you? I was studying for my calculus final and stumbled upon a peculiar function. Now I have to find the area bounded by the function (x^2+y^2)^3=xy^4 using a double integral. Now, the problem is that the graph is totally unknown to me (I have some ideas but I am not shure). A...

Hey guys, how are you? I was studying for my calculus final and stumbled upon a peculiar function. Now I have to find the area bounded by the function (x^2+y^2)^3=xy^4 using a double integral. Now, the problem is that the graph is totally unknown to me (I have some ideas but I am not shure). A...

Homework Statement Integrate f(u,v)= v - sqrt(u) over the triangular region cut from the first quadrant by the line u+v=64 in the uv plane. Homework Equations I am assuming u is the equivalent of the x-axis in the xy plane and v the equivalent of y in the xy plane. I am taking the...

Homework Statement Find the volume of the region common to the intersecting cylinders ##x^2 + y^2 = a^2## and ##x^2 + z^2 = a^2##. The Attempt at a Solution I am totally stuck here. What do they mean when they say 'intersecting cylinders'? I've drawn graphs of circles of radius a...

Homework Statement Find the volume of the region bounded by the elliptic paraboloid z = 4 - x^2 - \frac{1}{4}y^2 and the plane z = 0. Homework Equations -The Attempt at a Solution I'm not really sure where to start with this. This is how they've set it up: 4 \int_{0}^{2} \int_{0}^{2 \sqrt{4 -...

Homework Statement I know how to find the volume of a sphere just by adding the areas of circles, so I decided to do a double integral to find the same volume, just for fun. Here's what I've set up. I put 8 out front and designed the integrals to find an eighth of a sphere that has its center...

Homework Statement Let B \in ℝ2 the region is bounded by x^2 + y^2 = 4, \ x^2 + y^2 = 1, \ x^2 = y, \ 2x^2 = y evaluate \iint \limits_{B}\frac {2x^2+y^2}{xy}The attempt at a solution I needed to get the limits of integration. I used the following formula to start with: \iint...

Homework Statement Calculate \int \int x dx dy Over the area defined by 1 \leq x^{2} + 4y^{2} \leq 9 Homework Equations The Attempt at a Solution First we'll do the sub: u = x + y v = sqrt(3)y Which gives us the area 1 \leq u^{2} + v^{2} \leq 9, u,v\geq0 and the integral \sqrt{3} \int...

Homework Statement \int^{1}_{0}\int^{e^x}_{e^-x}\frac{lny}{y}dydx The attempt at a solution So I am integrating ln(y)/y and I tried it by parts, first with u = ln(y), dv = 1/y, and therefore du = 1/y, and v = ln y but if I use that I get (ln(y))2-\int\frac{lny}{y} again. So I tried...

I want the answer for this and how is it solved. double integral(x2+y2 dxdy) over the region in pos quadrant for which x+y<=1.

double integral help?? Homework Statement Evaluate the double integral | | e^sin(x) dA over the region D = {(x,y) | 0 ≤ x ≤ π/2, 0 ≤ y ≤ cosx} . Homework Equations The Attempt at a Solution how would i do this? i know that dA = dy(dx) so the integral would be |(0 ≤ x ≤ π/2) |(0 ≤ y ≤...

Homework Statement (X,Y) is uniformly distributed over the area T = {(x,y): 0 < x < 2, -x < 2y < 0} Find the marginal probability functions ie f_{x}(x) and f_{y}(y). The Attempt at a Solution The thing I'm having trouble with is that y depends on x. Am I supposed to rewrite the...

Homework Statement Homework Equations The Attempt at a Solution Solution is given. I don't understand how +-∏/4 is found as a range for θ Also why is 0 <= r <= cos2θ r is always r which is defined as cos2θ

Is there any rule of thumb for which variable should be integrated first?, i.e. to make the whole process of double integration easier.

Homework Statement find volume of the solid bounded by the surfaces z = 1- \sqrt{\frac{x}{4}^2 + \frac{y}{2 sqrt{2}}^2} and x^2/4 -x +(Y^2)/2 = 0 and the planes z = 0 and z = 1 Homework Equations z = 1- \sqrt{\frac{x}{4}^2 + \frac{y}{2 sqrt{2}}^2} and x^2/4 -x +(Y^2)/2 = 0...

Hello MHB, I got problem understanding how they can do this. $$\int_0^1\int_x^1 \sin(y^2)dydx$$ and rewrite it as $$\int_0^1\int_0^y \sin(y^2) dxdy$$ What I have done is. Then function is continuous ($$\sin$$ is a trig function) on a type I region D. We got $$D= (x,y)| 0\leq x \leq 1, x \leq y...

Hello MHB, I wanted to 'challange' myself with solve a problem with midpoint and rule and the double integral f over the rectangle R. This is a problem from midpoint. "Use the Midpoint Rule m=n=2 to estimate the value of the integrab $$\int\int_r(x-3y^2)dA$$, where $$R= {(x,y)| 0\leq x \leq 2, 1...

So I have to evaluate the integral from y=0 to y=1 of(the integral from x=(y^(1/2)) to x=1 of ((x^3)+1)^(1/2)dx)dy. I've substituted the ((x^3)+1) with sec^2(u) since I used tan^2(u)=x^3. I'm wondering if this is the correct (or even a good) manner of solving this because I'm ending up with a...

Calculate the double integral[FONT=Times], where D is the set of all points in the first quadrant which satisfies the inequality . [FONT=Times]I am confused how to calculate the a,b $$\int_a^b$$ (I don't know what you call that in english) Shall I do like this $$y=4-x$$ and put it in the...

Folks, Self reading a book in which an equation is given as I_{mn}\equiv\int_{\Delta} x^m y^n dx dy where we are integrating an expression of the form x^m y^n over an arbirtrary triangle. Is the above actually a double integral because of the dxdy term? Ie can this be written...

Homework Statement This is a 2 part question. I'm fine with the first part but the 2nd part I'm struggling with. The first part asks us to calculate the double integral, \int\intDx2dA for, D = {(x,y)|0≤ x ≤1, x≤ y ≤1} For this part I got an answer of 1/4. For the 2nd part we introduce a new...

Homework Statement Let R = \{ (x,y) \in \mathbb{R^{2}}: 0<x<1, 0<y<1\} be the unit square on the xy-plane. Use the change of variables x = \frac{{\sin u}}{{\cos v}} and y = \frac{{\sin v}}{{\cos u}} to evaluate the integral \iint_R {\frac{1} {{1 - {{(xy)}^2}}}dxdy} Homework Equations...

Homework Statement Evaluate ∫(0-1)∫(sqrt(y)-1) (ye^(x^2))/x^3 dx dy Homework Equations The Attempt at a Solution First, factor out the y for the inner integral, making ∫(0-1) y∫(sqrt(y)-1) (e^(x^2))/x^3 dx dy And evaluating the inner integral first: y∫(sqrt(y)-1)...

Homework Statement Use a double integral to find the area of one loop of the rose r = cos 3\theta Homework Equations The Attempt at a Solution This is a past test question. The only thing I got wrong was the set up while I got the rest of the mechanical steps right. I set up as...

This problem has brought something up that's making my brain wrinkle. It says to find the integral for $$\int_{ }^{ }\int_{D}^{ }xy\,dA$$ where \(D\) is the region bounded by \(y=x\), \(y=2x-2\), \(y=0\). I have to find the \(dx\,dy\) integral and then find the \(dy\,dx\) integral and evaluate...

Homework Statement Set up an integral for the ∫∫xydA for the region bounded by y=x, y=2x-2, and y=0. Set up the dxdy integral, then the dydx integral, then evaluate the simplest of the two. Homework Equations The Attempt at a Solution I drew the region which was easy enough, and...

I've done this problem and I have a feeling it's incorrect. I've never done a problem like this so I am kind of confused on how else to go about doing it. The goal is to change the cartesian integral $$\int_{-a}^{a}\int_{-\sqrt{a^2-x^2}}^{\sqrt{a^2-x^2}}\,dy\,dx$$ into an integral in polar...

Homework Statement Evaluate the double integral integral ∫∫2x^2-xy-y^2 dxdy for the region R in the first quadrant bounded by the lines y=-2x+4, y=-2x+7, y=x-2, and y=x+1 using the transformation x=1/3(u+v), y=1/3(-2u+v).Homework Equations The Attempt at a Solution I've obtained the Jacobian...

Homework Statement Evaluate the integral using polar coordinates: ∫∫arctan(y/x) dA Where R={ (x,y) | 1≤ x2 + y2 ≤ 4, 0≤y≤x Homework Equations X=rcos(T) Y=rsin(T) r2=x2 +y2 The Attempt at a Solution First thing was drawing a picture of R, which I think looks like a ring 1 unit thick...

Homework Statement (exact wording from my homework set) Set up an iterated integral for the volume of the region which is above the plane z=5 and below the graph of f(x,y)=21-(x^2+y^2)^2. Pay attention to what the region of integration should be! Homework Equations Not sure. The...

Hi everyone! I really need help for this. I have to read a paper in economics where some parts I don't understand. Suppose: S \equiv [\alpha,\bar{\alpha}]x[y,\bar{y}] V^e(p_j,g_j,y+r(r\alpha)-T_j,\alpha)\equiv \underset{h}{\text{max}}U(y+r(r,\alpha)-T_j,p_jh,h,g_j;\alpha) And...

Is it possible to come up with a derivation of the surface area of a sphere without using a double integral? Most of the ones I've found seem to involve double integrals; For example, this was given as the "simplest" explanation in a thread from 2005: S=\iint...

Homework Statement Calculate the double integral int int xye^((x^2)(y)) , 0<= x <= 1 , 0<= y <= 2 Homework Equations Integral by parts uv - int vdu The Attempt at a Solution The answer in the back of the book is (1/2)((e^2) -3) , but I get (1/2)((e^2) -1) . I think I made a...