Double integral Definition and 574 Threads

[sloved]reversing order of integration of double integral qns. Homework Statement pls refer to attached picture. Homework Equations The Attempt at a Solution intially upper and lower limits are , x^2 < y< x^3 and -1<x<1 sketched y=x^2 and y= x^3. => sqrt(y) =x and cube root...

Homework Statement Convert to polar coordinates to evaluate \int^{2}_{0}\int^{\sqrt(2x-x^2)}_{0}{\sqrt(x^2+y^2)}dydxThe Attempt at a Solution Really I'm just not sure how to convert the limits of integration. I know \sqrt(2x-x^2) is a half-circle with radius 1, but I'm not really sure where...

Homework Statement The fluid level in the tank ((1/4)*(x-4)^2 + y^2 == 4) is 7 m on the left edge of the tank (where x=0) and 5 m on the right edge (where x=8). Find the equation of the plane of the liquid, and use a double integral to find the volume of liquid in the tank. [Hint: you should...

Homework Statement Use polar coordinates to find the volume of the solid enclosed by the hyperboloid -x^2-y^2+z^2=1 and the plane z=2. The Attempt at a Solution Solving for z of the equation of the hyperboloid I find z = Sqrt(1 + x^2 + y^2). Letting z = 2 to determine the curve of...

Homework Statement Let Ω ⊂ R^2 be the parallelogram with vertices at (1,0), (3,-1), (4,0) and (2,1). Evaluate ∫∫_Ω e^x dxdy. Hint: It may be helpful to transform the integral by a suitable (affine) linear change of variables. Homework Equations The Attempt at a Solution Ok...

Homework Statement Let Ω ⊂ R^2 be the parallelogram with vertices at (1,0), (3,-1), (4,0) and (2,1). Evaluate ∫∫_Ω e^x dxdy. Hint: It may be helpful to transform the integral by a suitable (affine) linear change of variables.Homework Equations The Attempt at a Solution Ok here is what I have...

Homework Statement Evaluate \int\intT (x^2+y^2) dA, where T is the triangle with the vertices (0,0)(1,0)(1,1) Homework Equations The Attempt at a Solution \int d\theta \int r^3 dr Thats how far I got, not really sure about boundries on r. First integrals boundrie should be 0 to pi/4. Is...

\int_{0}^{\infty}fdx\int_{\frac{x-tx}{t}}^{\infty}dy=\int_{0}^{\infty}dx\int_{\frac{x-tx}{t}}^{\infty}fdy f is a function of x and y can i move f like i showed? can i change the order of integration ?

Homework Statement By transforming to polar coordinates, evaluate the following: \int^{a}_{-a}\int^{\sqrt{}{{a^2}-{x^2}}}_{-\sqrt{{a^2}-{x^2}}}dydx Homework Equations The Attempt at a Solution I can get the right answer to this but only after guessing that the inner limits...

Homework Statement sketch the region of integration, and evaluate the integral by choosing the best order of integration \int^{8}_{0}\int^{2}_{x^{1/3}}\frac{dydx}{y^{4}+1} Homework Equations integration by parts The Attempt at a Solution after sketching the graph and changing the...

Homework Statement All that is provided can be found through the following link: http://img33.imageshack.us/img33/6343/question2q.jpg Homework Equations No specific equations pertaining to solving double integrals. The Attempt at a Solution Ok, so I know that we cannot...

Hi, I am actually not really concerned about what the whole details are but more whether my approach is correct to show the following statement: Let f be continuous on a closed bounded region \Omega and let (x_0 ,y_0) be a point in the interior of \D_r. Let D_r be the closed disk with center...

1. Homework Statement [/b] Use the transformation that takes the unit square to a triangle to compute the integral \int\int_{B}2x+3y dA Where B is a triangular region with vertices (0,0), (5,2), and (3,4). The Attempt at a Solution What I did was I drew the region on an xy...

what'd I do wrong? I was told I didn't include the bound y<=x but that still hasn't helped me figure out where I miss stepped thanks -Ben

Homework Statement http://img23.imageshack.us/img23/3118/intx.th.jpg Homework Equations I'm guessing polar conversion? http://en.wikipedia.org/wiki/Polar_coordinate_system#Converting_between_polar_and_Cartesian_coordinates The Attempt at a Solution I'm having trouble tackling...

Homework Statement I don't know what is going on on my brain. I am at a sage in a problem where I need to evaluate the double integral: \int\int_S(x+z)\,dS where the surface is the is the portion of the plane x+y+x=1 that lies in the 1st octant.The Attempt at a Solution Forging ahead I...

\int_0^1\int_0^y e^{x^2} dx dy The region I am integrating over should look like this graph, right? I tried switching the bounds but I am left where what I started. since 0 < x < y, and 0 < y < 1 I can switch to 0 < x < 1 , and x < y < 1 leaving me with the integral...

Homework Statement Hey all. The problem is to solve the double integral xy da where the constraints C is x^2 + y^2 = 1, with the change of variables x = u^2 - v^2 and y = 2uv The problem is applying the change of variables to the constraint unit circle. After the algebra I end up with...

Homework Statement Calculate the double integral: \iint\limits_D x^{5}y^{6}dxdy where D = {(x,y): x9 ≤ y ≤ x1/9} Homework Equations The Attempt at a Solution I didn't think this problem would be too hard, but it seems I'm really not good with double integrals. Anyway, I...

Homework Statement \int_{D}\int y^2 where D = {(x,y) | -1 \leq y \leq1, -y-2\leq x\leq y The integral I set up is below : \int^{1}_{-1} \int^{y}_{-y-2} y^2 dx dy From that I get the answer 0, but the book says its 4/3. I get 0 because It reduces to this integral ...

Homework Statement integral of 1/(1-xy)dxdy x's from 0 to 1 and y's from 0 to 1 The Attempt at a Solution ok so the first integral gives -ln|1-y|/(y) after we evaluated the x's from 0 to 1 but I am having trouble with integrating with respect to y .

Homework Statement Evaluate the double integral sin(x-y)*e(x-y)^2-0y) 2--- dA where D is a disk of radius 2 whose center is (1; 1) Homework Equations The Attempt at a Solution gee this...

Homework Statement 1. Find the volume of the solid which is under the surface z = 2x + y2 and above the region bounded by x = y^2 and x = y^3. Homework Equations The Attempt at a Solution So first I graphed x=y^3 and x=y^2. (http://h.imagehost.org/view/0716/Math_Problem ) I found their...

I've tried this question with many different ways and i always got -11.576, but the autograder always marked it wrong. so hopefully i really did something wrong and you can teach me about it. find the double integral of -3*x*y - 3*y over the region bounded by x^2 + y^2 = 9, y = 3x, and y = 0...

Homework Statement I'm supposed to solve a definite double integral. It's supposed to be in the area of the triangle with vertexes at (0,0), (1,1),(0,2) Homework Equations integral of e^(y^2) * dy*dx The Attempt at a Solution First, I need to know the limits of x and y... So, that...

Homework Statement Homework Equations n/a The Attempt at a Solution I set up the intgral at integral from 0 to 5 of integral from 0 to 5y of 8e^(y^2)dxdy I solved it as an iterated integral so I solved the first part, then ended up with integral from 0 to 5 of 40ye^(y^2)...

Homework Statement bounded by x^2+y^2=r^2 and y^2 +z^2=r^2 i guess r is just a random constant Homework Equations The Attempt at a Solution i don't even have a clue of how to start this question

Homework Statement Rewrite by converting to polar coordinates, carefully drawing R. \int^{2}_{0}\int^{\sqrt{2x-x^2}}_{0}\sqrt{x^2+y^2}dydxHomework Equations The Attempt at a Solution I believe I have the inside part of it right. What I did was replace the x^2 and y^2 in \sqrt{x^2+y^2} with...

I need to find the area between the parabolas x=y^2 and x=2y-y^2, I know I need to use a double integral but am having difficulty finding the limits. Can anyone help please?

Homework Statement Solve: \iint_{\frac{x^2}{a^2}+\frac{y^2}{b^2} \leq 1} \sqrt{1-\frac{x^2}{a^2}-\frac{y^2}{b^2}} dx dy Homework Equations Cartesian to Polar The Attempt at a Solution Well - this Integral should be solved as a polar function (the radical should be...

I have come across the following integral which I need to compute: \int_0^{t_1} \int_{\nu_0}^{\infty} \left(\frac{h \nu ^3}{c^2}\right) \frac{1}{e^{\frac{h\nu}{k T(t)}}-1} d\nu dt The problem is, since the inner integral cannot be computed analytically, I have to resort to numerical...

Example: Use a double integral to find the area of the region: One loop of the rose r = Cos[3 theta] Finding the bounds of r is easy, 0 to Cos[3x]. However, I usually get the bounds of theta wrong. How do I find the bounds of theta without using a graphing calculator and guessing. The...

Homework Statement \int\int(rsin2\vartheta)drd\vartheta sorry i don't see how to put the bounds in but they are 0<\vartheta<\pi/2 and 0<r<2acos\vartheta Homework Equations I know that r=sin\varthetaThe Attempt at a Solution Im really not sure where to start my text is terrible. I really...

For the double integral \int\int_R sqrt(x^2+y^2) dx dy where R is the unit circle. I got\int_0^\pi\int_1^1 sqrt(r2) r dr dtheta Then after the integration I got an answer of 2pi/3 as my final answer. Is this right. The bottom of the 2nd integral is -1 not 1

How do I evaluate double integral as the limit of a sum: \int\int 1 dA with a snowflake region constructed as follows: Step 1: Start with a square of area 1 unit2. Step 2: Divide each edge into 3 and construct a smaller square on the middle third, thus creating new edges. Step 3: Repeat step 2...

Homework Statement Recall that the integral from -∞ to +∞ of e^(-x^2) is equal to the square root of Pi. Use this fact to calculate the double integral of e^-(x^2 + (x-y)^2 + y^2) dx over the entire region R2. Homework Equations The Attempt at a Solution I am not sure if it's...

Homework Statement The distribution of mass on the hemispherical shell z=(R2 - x2 -y2)1/2 is given by \sigma= (\sigma0/R2)*(x2+y2) where \sigma0 is constant. Find an expression in terms of \sigma0 and R for the total mass of the shell Homework Equations The mass is given by double...

question: how do i find the area under f[x,y] bounded by a closed parametric curve x[t],y[t]? it doesn't look like i can use a change of variables. it seems as though double integrals only with functions where the curve is given explicitly such as y[x] or x[y].

Homework Statement I am getting rather confused when I attempt to solve one of these double integral problems. A typical problem is phrased like this: If R = [-1, 3][3,5], use a Riemann sum with m = 4, n = 2 to estimate the value of the following \int\int(y^{2}-2x^{2} The problem will...

Evaluate a "simple" double integral Homework Statement Evaluate the double integral of f(x,y) = square root (1 - x^2 - y^2) over the disk centred at the origin of radius 1 Homework Equations The Attempt at a Solution So the disc of radius one has boundaries x^2 + y^2 = 1 i am...

Homework Statement Let f(x,y) = 1 if x = 1/3 and y is rational, and let f(x,y) = 0 otherwise. Show that the double integral of f over the region Q = [0,1]x[0,1] in R2 exists (SSQ f dA exists) yet the integral from 0 to 1 of f(1/3, y) does not exist. (sorry for the weird way of writing, I'm...

\int^{B}______________{A}\int^{\infty}_______________{0}\frac{t^{N-1}x^{s-N-1}dtdx}{e^{t+x}+1} With the restrictions that that B>A, 0<Re(s)<1 and N is a natural number>1. I think t=ab and x=a(1-b) would work, but I'm not sure how to go from there. I don't need to solve the integral; just...

\int_{c_1}^{c_2} \int_{g_1 (x)}^{g_2 (x)} f(x,y) dy dx If f(x,y) is function such that it is not easily integrable, if we wanted to switch the bounds of integration so that h1(y) = g1(x) , same for g2(x), what would be the general way to rewrite the bounds? Would it involve inverse...

Homework Statement given two surfaces S1={(x,y,z)|z=50-X^2} S2={(x,y,z)|z=9y^2+16} find the volume 1.V1 bounded above by S1 and below by S2 and on the sides by the vertical planes X=1 X=-1 Y=1 Y=-1 2 the solid V2 bounded above by S1 and below by S2 and on the sides by the vertical...

Homework Statement Find the volume of the solid bounded by z = 0 and z = 2xy, lying in the first quadrant and bounded by the curves y = x^2 and x+y = 2 Homework Equations The Attempt at a Solution I have an answer, but just asking if I've done it correctly, since we arent given the...

Homework Statement Use an appropriate double integral and the substitution y = br\sin \theta \text{\ \ \ } x = ar\cos \theta to calculate the bounded area inside the curve: {\left( \frac{x^2}{a^2} + \frac{y^2}{b^2} \right)}^2 = \frac{x^2}{a^2} - \frac{y^2}{b^2} (you can...

Homework Statement Need to integrate using the dirac delta substitution: \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\!x^2\cos(xy)\sqrt{1-k^2\sin^2(y)}\, dx\, dy Homework Equations \cos(xy) = \frac{1}{2}\left(e^{ixy} + e^{-ixy}\right) \delta\left[g(t)\right] =...

Homework Statement Use polar coords to evaluate the double integral x3 + xy2dydx from y = -(9-x2)1/2 to (9-x2)1/2, and x = 0 to 3 Homework Equations The Attempt at a Solution So the region is a half circle of radius 3, centered @ the origin, with only the possitive x side...

http://www.freeimagehosting.net/image.php?6417d9b089.gif i don't know what it means? what it actually does ? how to explain its function in words ??

why there are a case where double integral could calculate area and in other case it could calculate a volume. an integral should do only one thing not both?? for what characteristics it could used to calculate area, for what its volume