Find an approximation of the area of the region R under the graph of the function f on the interval [0, 2].

Question

Find an approximation of the area of the region R under the graph of the function f on the interval [0, 2]. Use n = 5 subintervals. Choose the representative points to be the midpoints of the subintervals.

f(x) = x² + 8

Answer 1

n=5, midpoints are .2, .6, 1, 1.4, 1.8

square each

add 8 to each

sum the squares+8(5)

times 2/5=.4

area= .4(8.04+8.36+9+9.96+12.24)=47.6(.4)=19.04

integral= x^3/3 +8x

from 0 to 2 = 8/3+16= 18.666...

off by 0.37333...