Chapter 21, Problem 14P

Evaluate the following double integral:

${\displaystyle {\int }_{-1}^1{\displaystyle {\int }_0^2\left(x^2-2y^2+x{y}^3\right)}dxdy}$

(a) Analytically;

(b) Using a multiple-application trapezoidal rule, with n = 2; and

(c) Using single applications of Simpson's 1/3 rule.

For (b) and (c), compute the percent relative error $\left({\epsilon }_t\right)$.