Approximate the area of the following using the indicated Riemann Sum.

Question

f(x) = 2x + 1 on [0,1] using 5 rectangles and using the right Riemann Sum.

Answer 1

base of each rectangle = 1/5

right side of each rectangle is

1/5, 2/5, 3/5, 4/5 and 5/5

heights are

11/5, 12/5, 13/5, 15/5 and 10/5

add them

65/5 =13

multiply by 1/5 to get 13/5 = 2.6 = area approximation which should be a little higher than the exact area

integral of 2x+1 = x^2 + x = 1 + 1 = 2

the area = sum of a triangle 2 x 1 = (2)(1)/2 = 1 plus a 1x1 rectangle = 1+1 = 2