Question

The given curve is rotated about the y-axis. find the area of the resulting surface. y = 1 3 x3/2, 5 ≤ x ≤ 12

Answer 1

The area of the resulting figure will be given by:
∫f(x)dx
f(x)=13/2x^3
thus
∫f(x)dx=13/2∫x³dx=13/8[x^4]
integrating over the inerval
13/8(12^4)-13/8(5^4)
=32680+3/8 sq. units
=