Question

Find the volume of the solid formed by revolving the region bounded by the graphs of y = x^2, x = 4, and y = 1 about the y-axis.

*answer choices in pic file below*

Answer 1

@Preetha can u plz help? :)

Answer 2

@Data_LG2

Answer 3

Well you could approach this with the Disk method or the Shell method.

Disk:
So the volume is
\[V=\int_{y}\pi\left[(\text{outer function})^2-(\text{inner function})^2\right]\,dy\]
The outer function is simply "4" , a constant. The inner function is \(y=x^2\). But since the integral is in terms of \(y\), it means \(x=\sqrt{y}\) (don't need to worry about the negative branch, since both x and y are \(>0\) (in 1st quadrant).
\[V=\int_0^1\pi \left[ 4^2-\left(\sqrt{y}\right)^2\right]\, dy \]

Actually this method is easier than the shell method since you'd have to split the integral into two regions which is slightly more work.