Question

Can someone answer this question please?

Answer 1

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.