Practice section 3 of 9

Find the value of the area of the region bounded by $y=\sin^{-1}x$ and the lines $x=0$, $y=-\pi/4$ and $y=\pi/3$.

Find the area of the region bounded by $1-x=(y+1)^2$, the y-axis, and the lines $y=-3$ and $y=2$.

Find the exact area of the region enclosed by $y=2+x-x^2$ and $y=x+1$.

Without using a calculator, find the area of the region enclosed by $y^2=4x$ and $y=2x-4$.

Find the value of the volume of the solid generated by rotating the region bounded by $y=x^3-2x^2$ and the x-axis through four right angles about the x-axis.

Find the exact volume of the solid formed when the region bounded by $y=\tan^{-1}x$, the y-axis and $y=\pi/4$ is rotated through $360^\circ$ about the y-axis.