Integrals and double integrals?

Question

if ∫ [from -3 to -2]f(x)dx = 2 and

∫ [from -1 to 3] g(x)dx=3, what is the value of

∫∫(sub D)f(x)g(y) dA where D is the square:

-3(<=)x (<=)-2, -1(<=)y(<=)3?

Answer 1

Since it is a rectangular region you can seperate the double integral into two iterated integrals thanks to Fubini&#039;s Theorem:

∫∫_D f(x) g(y) dx dy ={ ∫(f(x) dx) } × { ∫( g(y) dy) } = 2×3 = 6