Solving the Integral of s*(4-s)^\frac{1}{2}

[yaho8888]

Homework Statement

Find the intergal of $$s*(4-s)^\frac{1}{2}$$

Homework Equations

$$\int s*(4-s)^\frac{1}{2} dx$$

The Attempt at a Solution

using u sub
u = 4-s
s = 4-u

$$\int (4-u)*(u)^\frac{1}{2} du$$

$$\int 4u^\frac{1}{2}*u^\frac{3}{2}$$

then what?

 

[EnumaElish]

You mean, $$\int (4u^\frac{1}{2}-u^\frac{3}{2})du$$

 

[yaho8888]

Yes, $$\int (4u^\frac{1}{2}-u^\frac{3}{2})du$$

to solve this do I just do the integral of the equation above then plug in 4-x for u?

 

[bob1182006]

yes, 4-s. I think your original integral was meant to be ds not dx right?

also when you made your u substitution du=-ds so your integral should be u^(3/2)-4*u^(1/2)