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 ?

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Answer 1 · 2018-07-28T15:17:08

#50.817\ \text{unit}^3#

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#