Question

Find the area lying above the x-axis and below the parabolic curve y=4x-x^2

Answer 1

Finding the parabolas roots.
-x^2+4x=0
-x(x-4)=0
x=0 and x=4

$\int\limits^4_0 {(-x^2+4x)} \, dx$
$[-x^3/3+2x^2]$ (top is 4 and bottom is 0)
-64/3+32=32/3

The area above the x axis is 32/3