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

Answer:

A≅562.45π u²

Step-by-step 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 = $\frac{2}{3}x^{3/2}$

evaluated (60,77), then

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