Question

Find the area of the region bounded by the curves y=x³ and y=2x² between their intersections.

Answer 1

Hi,

answer 4/3

Explanation:

1. finding the intersections

`x^3-2x^2=x^2(x-2)\\x=0\ or \ x=2`

2. y=2x² is over y=x^3 between their intersections

`\int\limits^0_2 {2x^2-x^3} \, dx =\Big [\[ }(2x^3)/(3) -(x^4)/(4) \Big{]}_0^2\\\\=(16)/(3)-(16)/(4) -0\\\\=(4)/(3)`