The area of a region R is given by the iterated integrals . Switch the order of integration and show that both orders yield the same area. What is this area?

Question

The area of a region R is given by the iterated integrals  . Switch the order of integration and show that both orders yield the same area. What is this area?

Quizplus · Accepted Answer

Switching the order of integration, we have:

$\int_0^4\int_0^{\sqrt{x}}11e^{x^2+y^2}dydx=\int_0^2\int_{y^2}^{4}11e^{x^2+y^2}dxdy$

Both integrals evaluate to

$\frac{1}{2}(e^{16}-1)(e-1)\approx 64.019$

Thus, the correct answer is (C) 64.

The Area of a Region R Is Given by the Iterated