Find the volume of the solid formed by rotating the region enclosed by?

Question

Find the volume of the solid formed by rotating the region enclosed by

x=0, x=1, y=0, y=3+x^7

about the x-axis.

Answer 1

dV = [π(3 + x^7)^2]dx

dV = π(9 + 6x^7 + x^14)dx

V = π[9x + (3/4)x^8 + (1/15)x^15] | from x=0 to x=1

V = π[9(1 - 0) + (3/4)(1 - 0) + (1/15)(1 - 0)]

V = π(540 + 45 + 4)/60

V = π(589/60) ≈ 30.83997 cubic units