Double integral Definition and 558 Threads

I've written all the questions in the PDF file ... Please help me !

Homework Statement \int^{0}_{-3}\int^{\sqrt{9 - x^2}}_{- \sqrt{9 - x^2}} \sqrt{1 + x^2 + y^2} dy dx Homework Equations x = rcos(theta) y = rsin(theta) The Attempt at a Solution By making \sqrt{9 - x^2} = y then changing it to polar coordinates, I got r to be +/-3 but I'm...

Homework Statement Find the volume of the solid in the first octant by the planes z = x + y + 1 and z = 5 - x - y Homework Equations The Attempt at a Solution How would I set this up?

Homework Statement A lamina occupies the region inside the circle x^2 + y^2 = 2y but outside the circle x^2 + y^2 = 1. Find the center of mass if the density at any point is inversely proportional to its distance from the origin. Homework Equations Xcm = double integral of y*f(x,y)...

Homework Statement Consider the volume of a solid bounded by the cone: z = sqrt(x^2 + y^2) and the top half of the sphere x^2 + y^2 + z^2 = 18 that is for z >= 0 Using cylindrical coordinates, express the volume as a double integral. Homework Equations easy to sketch.. we can...

Homework Statement ok change the region R = { (x,y) | 1 <= X^2 + y^2 <= 4 , 0 <= y <= x } to polar region and perform the double integral over region R of z=arctan(y/x)dA Homework Equations r^2 = x^2 + y^2, x = r*sin(@), y = r * cos (@) The Attempt at a Solution i got R = {...

Homework Statement a) A lamp has two bulbs of a type with an average lifetime of 1000 hours. Assuming that we can modelthe probability of failure of these bulbs by an exponential density function \mu = 1000, find the probability that both of the lamps bulbs will fail within 100 hours. b)...

Hi, I was just wondering if the set up for this problem; integrate f(s,t)=e^slnt over the region in the first quadrant of the st-plane that lies above the curve s=lnt from t=1 to t=2 is: integral(t=1 to t=2)integral(s=ln1 to s=ln2) of e^slnt If that's not the right set up what am I...

simple question, for "find the area of the region between the xy-plane between the curves y=x3 and x=y2 where 0<x<1 , 0<y<1 is this the double integral for x3*y2 dy dx or for the double ingeral between x3+y2 dy dx?? i assume the first one? clarification needed please, can do the rest of the...

Homework Statement Basically I'm just trying to convert a double integral into polar coordinates, but when I do it I get confused with my bounds. Homework Equations The Attempt at a Solution 4\int_0^{\infty}\int_0^{\infty}e^{-(u^2+v^2)}u^{2x-1}v^{2y-1}dudv (x and y are just numbers, not...

Homework Statement The equation is \int^{t}_{0}[SIZE="6"]e^{-t'\gamma}\int^{t}_{0}[SIZE="6"]e^{t''\gamma}f(t'')dt''dt'. f(t) is a random function with no known anti-derivative. I need to simplify this into a single integral of one variable. Homework Equations above. The Attempt at a...

Homework Statement I have to solve the integral of (ytan^-1(x) - 3) inside the area of the rectangle with vertices (1,0), (0,1), (2,3), (3,2). How do I set up these limits? Homework Equations This is a tilted rectangle so I can't use just values for the limits? The Attempt at a...

Hi, I have a question about using the dirac function in a double integral. Lets say you have the double integral over the two values x1 and x2: int( int( sin(x1) * dirac(x1-x2) * sin(x2) )) Does this just simplify to a single integral: int( (sin(x1))^2 ) thanks!

Homework Statement Evaluate an iterated integral by reversing the order of integration \int^1_0\int^1_{y^2} ysin(x^2)dxdy Homework Equations The Attempt at a Solution I've got that the limits for x is between y^2 and 1, while the limits for y is between 0 and 1. Then I graphed...

Homework Statement Find the volume of the solid enclosed by the cylinders z=x^2, y=x^2, and the planes z=0 and y=4. Homework Equations The Attempt at a Solution ∫∫ x^2 dA For the limits of integration, I obtained y=x^2 and y=4, x=0 and x=2 I changed the order of...

Homework Statement Given the integral: \int_1^2\int_{\frac{3}{\sqrt{x}}}^{\sqrt{3}x}{{(x^2+y^2)}^{\frac{3}{2}}}dy \; dx. Convert to polar and evaluate. Homework Equations r=\sqrt{(x^2+y^2)} The Attempt at a Solution Ok, I've gotten bounds on \theta, \frac{\pi}{6} \le \theta \le...

Homework Statement \int\int_B 1 dx dy where B is the region enclosed by x^2 + y^2 = 9? What if B is the region eclosed by y = x +3, y = 5 - x, and y=8 Homework Equations The Attempt at a Solution So for x^2 + y^2 = 9, does it mean that both x and y go from -3 to 3? bot...

Homework Statement Evaluate the following integral: \int \int_R x^3 y^4 dx dy Homework Equations The Attempt at a Solution I don't even know where to start. My professor just introduced us to double integrals, now there's a strike going on at my school, so classes are...

How do you solve the double integral of xe^(xy)? bounded by x=0, y=1, x^2-y=0. I used both x-simple and y-simple methods but neither worked..I don't know what the limits are...thanks!

can someone please give me some help on this integral. it should be solvable analytically. \int^{1}_{-1}\int^{2\pi}_{0}\frac{1}{2+x+\sqrt{1-x^2}cos(y)+\sqrt{1-x^2}sin(y)}dxdy

Homework Statement How do you solve the double integral of cos(u/v) dudv, if the limits of u are v and -v, and the limits of v are 1 and 2? I tried doing it by parts but I didn't get it...

Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help! I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is...

Homework Statement \int\int x^2 dA where the area D is boundd by the ellipse 5x^2 + 4xy + y^2 = 1. Homework Equations The Attempt at a Solution I'm not sure where to start this question. A few ideas I'm exploring are: 1. rewrite in polar co-ordinates (not sure how to write an...

Homework Statement \int\int e^(^x^2^+^y^2^) dA where D is the region bounded by y = sqrt(1-x^2) and y = |x|. Homework Equations The Attempt at a Solution Obviously I can draw this region out and see what it looks like, and I will have to split the integral into two for negative...

Homework Statement Apply Green's Theorem to evaluate this integral: Integral of: (6y + x) dx + (y + 2x) dy over the curve C, where C is: The circle (x - 2)^2 + (y - 3)^2 = 4 Homework Equations The Attempt at a Solution To use Green's Theorem for this I would need to figure...

This is not for a specific problem, just in general: If we want to find the double integral of a function of two varaible, when we got other 1 varaible function to define the domain. What are the basics of drawing the domain in 2d (x, y only)?

Homework Statement Given the integral shown (in attachment), make a sketch of the region of integration, express the integral with the order of integration reversed and evaluate the integral after reversing the order of integration Homework Equations The Attempt at a Solution So...

Homework Statement Given the integral (shown in attachment) make a clear sketch of the region of integration and express the integral with the order of integration reversed. Evaluate the integral you found in (ii). Homework Equations The Attempt at a Solution Everything is in...

Homework Statement Use the transformation u = 3x + 2y and v = x + 4y to evaluate: The double integral of (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 = -(1/4)x, and y = (-1/4)x + 1. Homework Equations...

Consider the double integral \int_{-\infty}^{\infty}dx f(x) \, \int_{-\infty}^{\infty}dy g(y) The first one gives 0 the second one gives infinity (diverges). Then how to express the result of the integral? Is it 0 or infinity or neither (indeterminate)? Any other comments about the integration?

Homework Statement Consider the integral shown in the sketch. Sketch the region of integration and express the integral with the reverse order of integration and evaluate it leaving your answer in surd form Homework Equations The Attempt at a Solution I shaded the area of integration but I...

Homework Statement \int_a^b\,dx\int_a^x\,dy should give area of a triangle, I can’t see how. The Attempt at a Solution \int_a^b\,dx\,{(x-a)} but then I won’t get 1/2 (ab)… (don't get the first brackets in latex between the two x)

Flux = Int B dA Why isn't this written as a double integral when we antidifferentiate over an areal?

Evaluate \int\ \int_R\ x^2e^ydA Over the rectangle R with vertices (0,0), (1,0), (1,3) and (0,3). My answer: \int\ \int_R\ x^2e^ydA = \int_0^3\ \int_0^1\ x^2e^ydA = \int_0^3\ [x^3/3]_0^1 e^y dy = 1/3 \int_0^3\ e^ydy = 1/3 (e^3-1) Double integrals are new to me, so if...

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 a cone is given by the formula (pi*R^2*H)/3 I...

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...