How to find the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, y=7+x^7 about the x-axis ?

1 Answer

50.817\ \text{unit}^3

Explanation:

The volume of solid generated by rotating the region bounded by x=0, x=1, y=0 & the curve y=7+x^7 is given as

\int \pi y^2\ dx

setting y=7+x^7 & using proper limits,

=\int_0^1 \pi (7+x^7)^2\ dx

=\pi\int_0^1 (x^14+14x^7+49)\ dx

=(x^15/15+7/4x^8+49x)_0^1

=(1)^15/15+7/4(1)^8+49(1)-0

=3049/60

=50.817\ \text{unit}^3