91Ó°ÊÓ

For the following exercises, graph the equations and shade the area of the region between the curves. Determine its area by integrating over the \(x\) -axis. $$ y=e^{x}, y=e^{-x}, x=-1 \text { and } x=1 $$

For the following exercises, graph the equations and shade the area of the region between the curves. Determine its area by integrating over the \(x\) -axis. $$ y=e, y=e^{x}, \text { and } y=e^{-x} $$

For the following exercises, graph the equations and shade the area of the region between the curves. Determine its area by integrating over the \(x\) -axis. $$ y=|x| \text { and } y=x^{2} $$

For the following exercises, graph the equations and shade the area of the region between the curves. If necessary, break the region into sub-regions to determine its entire area. $$ y=\sin (\pi x), y=2 x, \text { and } x>0 $$

For the following exercises, graph the equations and shade the area of the region between the curves. If necessary, break the region into sub-regions to determine its entire area. $$ y=12-x, y=\sqrt{x}, \text { and } y=1 $$

For the following exercises, graph the equations and shade the area of the region between the curves. If necessary, break the region into sub-regions to determine its entire area. $$ y=\sin x \text { and } y=\cos x \text { over } x=[-\pi, \pi] $$

For the following exercises, graph the equations and shade the area of the region between the curves. If necessary, break the region into sub-regions to determine its entire area. $$ y=x^{3} \text { and } y=x^{2}-2 x \text { over } x=[-1,1] $$

For the following exercises, graph the equations and shade the area of the region between the curves. If necessary, break the region into sub-regions to determine its entire area. $$ y=x^{2}+9 \text { and } y=10+2 x \text { over } x=[-1,3] $$

For the following exercises, graph the equations and shade the area of the region between the curves. If necessary, break the region into sub-regions to determine its entire area. $$ y=x^{3}+3 x \text { and } y=4 x $$

For the following exercises, graph the equations and shade the area of the region between the curves. Determine its area by integrating over the \(y\) -axis. \(x=y^{3}\) and \(x=3 y-2\).