Question

Use the upper and lower sums of 8 rectangles to find two approximations of the area between f(x)=(sqrtx)+2 and the x-axis over the interval [0,2]

Answer 1

so for the left sided triangles we have

(2-0)/8 = 1/4, so the base of our triangles will be (1/4)
and we want to multiply that by our height, which is given by f(x)
and since we want the left side, we have

(1/4)(f(0)+f(1/4)+f(2/4)+f(3/4)+f(1)+f(5/4)+f(6/4)+f(74/)) = ?

Answer 2

replace the word triangle with rectangle....sorry

Answer 3

similarly we have for the right

\((1/4)(f(1/4)+f(2/4)+f(3/4)+f(1)+f(5/4)+f(6/4)+f(7/4)+f(2)) = ?\)