I want to calculate the volume of solid formed by rotating the region R bounded by $$ y=1+\sqrt{x} ,x=0,x=9, y=0$$ about x-axis.
So, using disk-washer methods:
$$ \pi\int_0^9 (1+\sqrt{x})^2 dx= \frac{171}{2}\pi $$
while using cylindrical shell method:
$$2\pi\int_1^4 y(9-(y-1)^2)dy$$
which would yield a different answer. May I ask why?
Best Answer
You need to add $$2\pi \int_0^1 y\cdot 9 \, dy$$ to second integral.