What is the best method to solve a double integral, and can you provide an example with instructions on how to evaluate it?

Answer 1

Brian Craig

The best method to solve a double integral is to use iterated integrals, where the double integral is evaluated as two single integrals in sequence. For example, to evaluate ∫∫_D (x^2 + y^2) dA where D is the region bounded by x=0, x=1, y=0, and y=1, first integrate with respect to y, then with respect to x. The process involves setting up the integral as ∫ from 0 to 1 ( ∫ from 0 to 1 (x^2 + y^2) dy ) dx. Evaluate the inner integral, then the outer integral.