Sunday

December 21, 2014

December 21, 2014

Posted by **Ryoma** on Monday, February 19, 2007 at 2:00pm.

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

**Answer this Question**

**Related Questions**

asdf - Find a definite integral indicating the area of the surface generated by ...

Math integral - What is the integral of 1/(x√(x^2-4)) dx? So I know that I...

calculus - LEt f and g be continous functions with the following properties i. ...

calculus - LEt f and g be continous functions with the following properties i. ...

Calculus - Use the shell method to set up, but do not evaluate, an integral ...

calculus - 2. Let R be the region in the first quadrant bounded by the graphs of...

calculus - 2. Let R be the region in the first quadrant bounded by the graphs of...

Calculus - Center of Mass - Find the exact coordinates of the centroid given the...

calculus - 8). Part 1 of 2: In the solid the base is a circle x^2+y^2=16 and the...

Calculus integral - evaluate the integral: integral from -pi/4 to 0 for the ...