Double integral Definition and 558 Threads

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...

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}...

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...

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...

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

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

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!)...

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...