The integral below represent the volume of a solid. Describe the solid. `int_0^1(2pix^9)dx`
The problem provides the definite integral `int_0^1 (2pix^9)dx` that helps you to evaluate the volume of a solid.
You should compare the given integral to the formula that helps you to evaluate the volume of a solid obtained by rotating around y axis the region under the curve `f(x) = y` , from a to b, using method of cylindrical shells, such that:
`V = int_a^b 2pi*x*f(x)dx`
You may write the given integral, such that:
`V = int_0^1 (2pix)*(x^8)dx`
Comparing the formula and the given integral, yields:
`f(x) = y = x^8`
`a = 0, b = 1`
The problem requests for you to identify what is the solid described by the given integral.
Hence, the solid requested is obtained by revolving the region `0 <= y <= x^8, 0 <= x <= 1` , around y axis.