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Magazine Problem 21
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. $$ x=2 y \text { and } x=y^{3}-y $$
Problem 22
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. $$ x=-3+y^{2} \text { and } x=y-y^{2} $$
Problem 23
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. $$ y^{2}=x \text { and } x=y+2 $$
Problem 24
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. $$ x=|y| \text { and } 2 x=-y^{2}+2 $$
Problem 25
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. $$ x=\sin y, x=\cos (2 y), y=\pi / 2, \text { and } y=-\pi / 2 $$
Problem 26
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 or \(y\) -axis, whichever seems more convenient. $$ x=y^{4} \text { and } x=y^{5} $$
Problem 27
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 or \(y\) -axis, whichever seems more convenient. $$ y=x e^{x}, y=e^{x}, x=0, \text { and } x=1 $$
Problem 28
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 or \(y\) -axis, whichever seems more convenient. $$ y=x^{6} \text { and } y=x^{4} $$
Problem 29
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 or \(y\) -axis, whichever seems more convenient. $$ x=y^{3}+2 y^{2}+1 \text { and } x=-y^{2}+1 $$
Problem 30
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 or \(y\) -axis, whichever seems more convenient. $$ y=|x| \text { and } y=x^{2}-1 $$
