Region of Integration
a) Sketch the region of integration and evaluate the following integral by converting it to
polar coordinates.
$$
\int_{-4}^{4} \int_{0}^{\sqrt{16-x^2}} cos(x^2 + y^2) dy dx
$$
Hint: x = r cos θ, y = r sin θ, dx dy → r dr dθ.
b) For the integral
$$
\int_{0}^{1} \int_{y}^{1} sin(x^2) dx dy
$$
i. Sketch the region of integration.
ii. Reverse the order of integration.
iii. Use the expression obtained in item 4(b)ii to evaluate the integral.