area between curves

Question

find the area between y=0 and y=3(x³-x) 

Answer 1

I took the integral from 1 to 0 to get

 

∫¹  0 - (3(x³-x)) dx

  ₀

 

As you can see I only evaluated the integral from 0 to 1 because part of the curve is above the x axis and the other part is below the x axis.  I will end up doubling the answer to get the  area since it is symmetric. 

 

For the integral -3(1/4 x⁴ - 1/2 x²)

 

This will give you an answer of -3[(1/4 - 1/2) - 0]

 

This comes out to -3(-.25)-0 which is .75.  Now I double it and the answer is 1.50.  That should be the area.