Question

Find the area of the surface generated when the given curve is rotated about the x-axis. y = 4 squareroot x on [60, 77] The area of the surface generated by revolving the curve about the x-axis is square units. (Type an exact answer, using it as needed.)

Answer 1

A≅562.45π u²

Explanation:

Knowing that the volume the a solid is V=πR²h, then A=πR², therefore

A=π(4√x), integrating on both sides ∫A=4π∫√xdx ⇒ ∫√xdx =
`(2)/(3)x^(3/2)`

evaluated (60,77), then

`A=(8\pi )/(3)(77^(3/2)-60^(3/2))\\A=(8\pi )/(3)(675.67-161.75})\\A=562.45\pi`