Steps: 1. calculate the values of y at x=0,1,2. using y=5-x^2 2. calculate the areas of trapezoids (Bottom+Top)/2*height 3. add the areas.
1. x=0, y=5-0^2=5 x=1, y=5-1^2=4 x=2, y=5-2^2=1 2. Area of trapezoid 1 = (5+4)/2*1=4.5 Area of trapezoid 2 = (4+1)/2*1=2.5
Total area of both trapezoids = (4.5+2.5) = 7
Exact area by integration: integral of (5-x^2)dx from 0 to 2 =[5x-x^3/3] from 0 to 2 =[5(2-0)-(2^3-0^3)/3] =10-8/3 =22/3 =7 1/3, slight greater than the estimation by trapezoids.
