Question

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.y = x + 1, y = 0, x = 0, x = 4; about the x-axis

Answer 1

V= 124π/3

Explanation:

V=∫πr²dx

• r=yx(x+1)
• integration limits are x=0 to x=4

This gIves:

=∫π(x+1)²dx

=∫π(x²+2x+1)dx

=π(x³/3+x²+x) |₀⁴

=π(4³/3+4²+4)-π(0³/3+0²+0)

=π(64/3+16+4)

=π(64/3+48/3+12/3)

=π(124/3)=124π/3