Definite integral

Question

Definite integral

fine the area of region bounded by the graph y1=x^2-2x , y2=2-x

Answer 1

find the limit of integration

2-x=-x^2+x+2

-x^2+x+2=0

x= -1,2

integral (2-x)-(-x^2-2x) dx (-1,2)

= -x^3/3+x^2/2+2x evaluate at upper and lower limit

( -(-1)^3/3+(-1)^2/2+2(-1))-( -(2)^3/3+(2)^2/2+2(2))=9/2