In Exercises 23-26, sketch the region of integration and convert each
polar integral or sum of integrals to a Cartesian integral or sum of
integrals. Do not evaluate the integrals.
$\int_0^{\pi/2} \int_0^1 r^3 \sin \theta \cos \theta \, dr \, d\theta$
$\int_{\pi/6}^{\pi/2} \int_1^{\csc \theta} r^2 \cos \theta \, dr \, d\theta$
$\int_0^{\pi/4} \int_0^{2 \sec \theta} r^5 \sin^2 \theta \, dr \, d\theta$
$\int_0^{\tan^{-1} \frac{4}{3}} \int_0^{3 \sec \theta} r^7 \, dr \, d\theta + \int_{\tan^{-1} \frac{4}{3}}^{\pi/2} \int_0^{4 \csc \theta} r^7 \, dr \, d\theta$
