91Ó°ÊÓ

[T] There is a curve known as the "Black Hole." Use technology to plot \(r=e^{-0.01 \theta}\) for \(-100 \leq \theta \leq 100\).

For the following exercises, determine a definite integral that represents the area. Region enclosed by \(r=4\)

For the following exercises, determine a definite integral that represents the area. Region in the first quadrant within the cardioid \(r=1+\sin \theta\)

For the following exercises, determine a definite integral that represents the area. Region enclosed by one petal of \(r=8 \sin (2 \theta)\)

For the following exercises, determine a definite integral that represents the area. Region enclosed by one petal of \(r=\cos (3 \theta)\)

For the following exercises, determine a definite integral that represents the area. Region below the polar axis and enclosed by \(r=1-\sin \theta\)

For the following exercises, determine a definite integral that represents the area. Region in the first quadrant enclosed by \(r=2-\cos \theta\)

For the following exercises, determine a definite integral that represents the area. Region enclosed by the inner loop of \(r=2-3 \sin \theta\)

For the following exercises, determine a definite integral that represents the area. Region common to \(r=2\) and \(r=4 \cos \theta\)

For the following exercises, determine a definite integral that represents the area. Region common to \(r=3 \cos \theta\) and \(r=3 \sin \theta\)