# Calculus II/III

posted by
**Ryoma**
.

A. Find the integral of the following function.

Integral of (x√(x+1)) dx.

B. Set up and evaluate the integral of (2√x) for the area of the surface generated by revolving the curve about the x-axis from 4 to 9.

For part B of our question , the surface of revolution is is

integral of 2 pi y * dx

= 4 pi x^(1/2) dx

for x from 4 to 9.

The indefinite integral is

4 pi x^(3/2)/(3/2)

For the definite integral, subtract the value at x = 4 from the value at x = 9.

Try making the subsitution u = x + 1

x = u -1

dx = du

The integral becomes

Integral of (u^3/2) - u^(1/2) du

= (2/5) [u^(5/2) - (2/3) u^(3/2)] du

= (2/5) (x+1)^(5/2) - (2/3)(x+1)^(3/2)]

For the part B of you question, integrate

2 sq