# Exercises - Area Between Curves

1. Find the area bound between the curves $y=x^2$ and $y=-x^2+4x$   in two different ways.

2. Find the area between $y=\sin x$ and $y = \cos x$, from $x=0$ to $x=\frac{\pi}{2}$

3. Find the area enclosed by the curves $y=x^3$, $y=-x$, and $y=-6x+20$   in two different ways.

4. Find the area between $y=\cos x$ and the $x$-axis from $x=-\pi$ to $x=2\pi$.

5. Find the area between $y=x^2-4x$ and the $x$-axis from $x=0$ to $x=6$.

6. Find the area between $y=\sin 2x$ and $y=\cos 2x$ from $x=0 to$x=\pi$. 7. Sketch the graphs showing the region enclosed by$y=5-x^2$and$y=x^2-2x+1$. Setup two expressions (one involving integral(s) in terms of$x$, the other involving integral(s) in terms of$y$) that will both give the area of the enclosed region. Find this area by evaluating one of these expressions. 8. Sketch the graphs showing the region enclosed by$y=x+4$and$y=x^2-2$. Setup two expressions (one involving integral(s) in terms of$x$, the other involving integral(s) in terms of$y$) that will both give the area of the enclosed region. Find this area by evaluating one of these expressions. 9. Find the area of the region between$y=x^2$and$x-2y=2$from$x=-2$to$x=1$. 10. Find the area of the region bounded by$f(y)=y^2$and$g(y)=4$. 11. Find the area of the region bounded by$x=3y+10$and$x=y^2$in two different ways (one involving integral(s) in terms of$x$, the other involving integral(s) in terms of$y$). 12. Find the area of the region bounded by$y=x^2-3x$and$y=x$. 13. Find the area bounded by$x=y^2$and$x=-y^2+2y+4$in two different ways (one involving integral(s) in terms of$x$, the other involving integral(s) in terms of$y$). 14. Sketch the region enclosed by$y=x^2-2x$and$y=-x^2+4$and then setup the integral(s) necessary to find the area bound by these curves. Do this in two ways: one using integrals in terms of$x$; the other using integrals in terms of$y\$.