What is Double integral: Definition and 573 Discussions

In mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z). Integrals of a function of two variables over a region in





R


2




{\displaystyle \mathbb {R} ^{2}}
(the real-number plane) are called double integrals, and integrals of a function of three variables over a region in





R


3




{\displaystyle \mathbb {R} ^{3}}
(real-number 3D space) are called triple integrals. For multiple integrals of a single-variable function, see the Cauchy formula for repeated integration.

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  1. B

    Double integral - change of variables

    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...
  2. S

    Solving Double Integral: Struggling with Variables

    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...
  3. T

    What Are the Limits of Integration for a Double Integral in a Triangular Region?

    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?
  4. M

    Finding Volume of Solid Bounded by Equations: How to Setup a Double Integral?

    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...
  5. E

    Help with this double 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
  6. B

    Evaluate the following double integral

    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...
  7. P

    Double integral to find the area of the region enclosed by the curve

    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
  8. S

    Evaluating a Double Integral: Finding the Volume of a Bounded Region

    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...
  9. M

    How can I set proper limits for a double integral?

    *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...
  10. M

    How can I improve my limit-setting skills for double integrals?

    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...
  11. J

    Double integral and polar coord

    Please help. Thank you.
  12. O

    Finding Volume of a Bounded Cylinder with Double Integral

    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...
  13. I

    Double Integral Substitution: Solving for the Jacobian in Terms of u and v

    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...
  14. H

    Interchanging integration bound for double integral

    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 ?
  15. H

    How Do You Integrate These Challenging Double Integrals?

    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...
  16. Cyrus

    Calculating Surface Area Using Double Integrals

    Hi, I have a question on the method of calculation of the surface area of a surface. I am using "Calculus Concepts and contexts by stewart", chapter 12.6. In it, he goes on to explain how to calculate the suface area of a surface as a double integral by using approximations. He breaks up...
  17. quasar987

    Double Integral of f(x,y) in a Triangle Domain

    I am asked to calculate the double integral of the function f(x,y) = (2x+3y)^2 = 4x^2 + 12xy + 9y^2 on the domain defined by a triangle whose summits(?) are at (-1,0), (0,1) and (1,0). I chose to integrate from left to right. So the bounds of my integral are \int_0^1 \int_{y-1}^{1-y}...
  18. L

    Calculating Volume with Double Integrals: Finding Limits for Enclosed Space

    Hi I am trying to find volume enclosed by following equations: z = 3x, //Top plane x^2 + y^2 = 25, // cylinder x = 4, //line parallel to y axis x, y=0. I am trying to figure out what "Limits" should I take on the "Double Integral" to get the below mentioned Volume ans. Ans...
  19. B

    Finding volume using polar coordinates

    Ok the question is find the volume of the region inside the surface z = x2 + y2 and between z = 0 and z = 10. Ok i have already found the limits of integration but i am having a hard time calculating the integral. The limits are -{\sqrt{10-x^2} <= y <= {\sqrt{10-x^2} -{\sqrt{10} <= x...
  20. G

    Double integral with absolute value of x-y

    int(int(abs(x-y)*6*x^2*y)) the range of x and y are 0,1. Normally i'd check to split it up and change the limits, but i think my brain is broken because I'm not seeing it at the moment. simple question that i need to know how to do for stats without using maple :P
  21. tandoorichicken

    How Do You Solve a Double Integral for Area Between z=e^{x^2} and the xy-Plane?

    I was just faced with this problem on a test and I have no idea how to do it Find the area between the xy-plane and z= e^{x^2} as bounded by x=0, x=1, and y=2x. I have no idea how to do this problem. I set up the integral as \int_{0}^{1} \int_{0}^{2x} e^{x^2} \,dy \,dx
  22. C

    Need Help with Double Integral Problem?

    Double Integral Problem... We've been given a question about double integrals and I'm confued by the integration needed and I figure I'm doing something really dozey because all the others have worked out with the exception of this one- (sorry I don't know how to do the integration signs!)...
  23. V

    When you transform a double integral that goes over a set

    Here's the deal: When you transform a double intergral that goes over a set D < RxR bounded on y-axes by g1(x) and g2(x) in two "normal" ones(litteral translation from my language would be subsequent integrals - don't know the word in English) how do you swap the integrals by x and by...
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