Find the volume of the solid obtained by rotating the region bounded by the curves
y = x^8, y = 1 about
the line y = 5.
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1 answer

intersection of y =1 and y = x^8 is (1,1) and (1,1)
because of the nice symmetry we could just go from 0 to 1 and double.
V = 2π∫ ( (5x^8)^2  (51)^2 ) dx from 0 to 1
= 2π ∫ (25  10x^8 + x^16  16) dx from 0 to 1
= 2π [9x  (10/9)x^9 + (1/17)x^17 ] from 0 to 1
= 2π(9  10/9 + 1/17  0)
= 2432π/153
check my arithmetic 👍
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answered by Reiny
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