Question

1.   Find the volume generated under the curve y=x^3 + 3 and the x-axis between x=0 and x=3, rotated about the x-axis.

Answer 1

The formula of finding the volume of the solid generated by revolving the curve about x axis is found by multiplying π by the integration of the square of the function in given interval.

V=π$\int$₀³(x³+3)²dx=π$\intop$₀³(x⁶+6x³+9)dx=π(x⁷/7+6x⁴/4+9x)/₀³=π(2187/7+486/4+27)=

=π6453/14