Question

Find the area of the region bounded by the parabola y=x2+1 and the lines y=x,x=0andx=2.

Answer 1

$\displaystyle\\A=\int \limits_0^2(x^2+1-x)\, dx\\\\A=\left[\dfrac{x^3}{3}+x-\dfrac{x^2}{2}\right]_0^2\\\\A=\dfrac{2^3}{3}+2-\dfrac{2^2}{2}-\left(\dfrac{0^3}{3}+0-\dfrac{0^2}{2}\right)\\\\A=\dfrac{8}{3}+2-2\\\\A=\dfrac{8}{3}$