Applications of definite integral

Find the area of the “smile” bounded by half the circle and half the ellipse (see the picture). Points $A$ and $B$ are the foci of the ellipse.

Find the area of the sickle bounded by half the ellipse and half the circle (see the picture). Points $A$ and $B$ lying on the circle are the foci of the ellipse.

The function $f(x)=\frac{1}{2}x+2$ is graphed in the picture. Consider the region between the graph of the function $f$, the $x$-axis and the lines $x=-2$ and $x=1$. Find the volume of the solid of revolution obtained by revolving this region about $x$-axis.

The instantaneous velocity of a moving body is proportional to the cube of the time. The velocity at the time $t=3\mathrm{s}$ is $v=9{\mathrm{m}\mathrm{s}}^{-1}$. What is the distance traveled by the body in the first $6$ seconds?