What is the approximate area of the region?

Question

Use the rectangles to approximate the area of the region. (Round your answer to three decimal places.)

f(x) = 9 - x^2 [-3,3]



Answer 1

Approximation is

(-1.5 - -3)*4 + (1.5 - -1.5)*8.5 + (3 - 1.5)*4 =

1.5*4 + 3*8.5 + 1.5*4 =

6 + 28 + 6 = 40

The integral is 9x - (1/3)x^3

x=3: 9*3 - (1/3)*3^3 = 27 - 9 = 18

x=-3: 9*-3 - (1/3)*(-3)^3 = -27 - (-9) = -18

The exact area is 18 - -18 = 36