calculas question |(integrals)?

Question

if f(x) = (SQRT x ) - 2, 1
answer is = -0.856759
i only know the answer, need the method.

thanks scarlet. it looks easier now. =/=

Answer 1

With n=5, the intervals will be
[1, 2], [2, 3], [3, 4], [4, 5], [5, 6]
each with width 1, and midpoints 1.5, 2.5, 3.5, 4.5, 5.5.
To get the Riemann sum, multiply the function value at the midpoint of each interval by the width of the interval, and add all those values together.
So we get 1.f(1.5) + 1.f(2.5) + 1.f(3.5) + 1.f(4.5) + 1.f(5.5)
= √1.5 - 2 + √2.5 - 2 + √3.5 - 2 + √4.5 - 2 + √5.5 - 2
= -0.856759381665893 to 15 d.p.

Answer 2

assuming you have the coordinates of the midpoints...
1. draw rectangles, width of one with there midpoint at the midpoints. add up the rectangles to find the reimann sum (i did this on the ap test:)