Calculus - Double Integral?

Question

Question : Sketch the region R and evaluate the double integral: (Area Integral) f(x,y) dA = (Area Integral) (x^2)*(y) dydx

Where (Area Integral) stands for the double integral and the bounds of the second written out integral is 0 (lower) to 1 (upper) for x, and (x)^(1/2) (lower) to 1 (upper) for y.

My difficulty is with trying to sketch this graph, how would I go about doing this?

Answer 1

get a software program called maple11 or maple 10.

http://www.maplesoft.com/products/Maple11/professionals/index.aspx

other than that, just graph the two function in the integral dy for the bounds of dx. I hope you understand that. the program will help, but it cost $100 unless you know how to download it for free.

Answer 2

The region is just the area above the curve y=sqrt(x) [a sideways parabola opening to the right] and below y=1, and between x=0 and x=1. Think of the actual f(x,y) as a hilly function rising into the third dimension above this little region. Now all that is required is to double integrate the hilly f(x,y) across the region so defined.