Question

**Calc 2 help needed** Find the area of the surface generated by revolving the curve y = sqrt( x + 1) from x = 1 to x = 5 around the x-axis.

Answer 1

we have
\[y=\sqrt{x+1}\]

at x= 1 y=\(\sqrt 2\)
at x = 5 y=\(\sqrt 6\)
let's draw the graph first

Answer 2

now for finding the volume let's take a recatngle with length length y and width dx
if we were to find the area
\[A=\int_{x=1}^{x=5} (\sqrt{x+1}-0) dx\]