Question

Find the volume of the solid generated by revolving the area bounded by y=x^2 and x-axis from [0,2] around the x-axis

Answer 1

Answer:
`(32\pi )/(5)\ \text{unit}^3`

Explanation:

Given

The area is bounded by
`y=x^2` and x-axis from [0,2]

The volume generated for
`y=f(x)` when rotated about the x-axis in the interval [a,b] is

`V=\int_a^b\pi y^2dx`

Insert the values

`\Rightarrow V=\int_0^2\pi x^4dx\\\\\Rightarrow V=\pi \int_0^2x^4dx\\\\\Rightarrow V=\pi \left[ (x^5)/(5)\right]_0^2\\\\\Rightarrow V=(2^5\pi )/(5)\\\\\Rightarrow V=(32\pi )/(5)\ \text{unit}^3`