Calculus 7.3 Shell Method

True or False: For the shell method $V\ =\ \pi\int_a^bp\left(x\right)h\left(x\right)dx$  

• True

• True, but only in some instances

• False, it is  $2\pi$  

• False, this is the disc/washer method

Use the shell method to find the volume of the solid generated by revolving the region bounded by  $y=\sqrt{x}$  and  $x=4$  and  $y=0$  about the y-axis.

•  $\frac{128\pi}{5}$  

•  $16\pi$  

•  $\frac{32\pi}{5}$  

•  $\frac{8\pi}{3}$  

Use the shell method to find the area of the region bounded by  $y=x^3$  and  $x=0$  and $y=8$  about the x-axis.

•  $\frac{768\pi}{7}$  

•  $\frac{32\pi}{5}$  

•  $\frac{32768\pi}{5}$  

•  $\frac{64\pi}{7}$  

Use the shell method to find the volume of the solid generated by revolving the region bounded by  $y=x^2$  ,  $y\ =\ 4$  and  $x=0$  about the y-axis.

•  $8\pi$  

•  $\frac{16\pi}{3}$  

•  $16\pi$  

•  $2\pi$  

Use the shell method to find the volume of the solid generated by revolving the region bounded by  $y=x^2$  and  $y=2x$  about the y-axis.

•  $\frac{8\pi}{3}$  

•  $8\pi$  

•  $6\pi$  

•  $\frac{4\pi}{3}$