Exercise 34

Express the double integral \(\iint_D xy\sqrt{1 + x^2 + y^2} dA\) in terms of a single integral with respect to \(r\), where \(D\) is the portion of the disk \(x^2 + y^2 \le 1\) that lies in the first quadrant. Then use your calculator to evaluate the integral correct to four decimal places.