Estimate the area

Question

Estimate the area under f (x) = 1 + x^2 from x = 3 to x = 3 using three rectangles and right endpoint.

Answer 1

Since the region is from -3 to 3 (distance of 6), separated into 3 rectangles, each rectangle is 6/3 = 2 wide (2 on the x).

Calculate the height of each rectangle from the right side of it, and use 2 as the width. Area is width * height.

Rectangle 1 goes from -3 to -1, and the height is calculated at -1: 1 + 1^2 = 2. 2 * 2 = 4 is the area.

Rectangle 2 goers from -1 to 1, and the height is calculated at -1: 1 + (-1)^2 = 2. 2 * 2 = 4 is the area.

Rectangle 3 goes from 1 to 3, and the height is calculated at 3: 1 + 3^2 = 10. 2 * 10 = 20 is the area.

Estimated area is 4 + 4 + 20 = 28.