For the function whose values are given in the table below, the integral from 0 to six of f(x)dx is approximated by a Reimann Sum using the value at the LEFT ENDPOINT value of each of three intervals with width 2.

Question

X 0 1 2 3 4 5 6
f(x) 0 0.25 0.48 0.68 0.84 0.95 1

The Approximation is:
a) 2.64
b) 3.64
c) 3.72
d) 3.76

Answer 1

That would be 2*(f(0)+f(2)+f(4))

Answer 2

you would add 0+0.48+0.84 and then multiple that by 2. Its those numbers because its asking for the left endpoint. If it were asking for the right endpoint, it would be 0.48+0.84+1 and multiplied by 2. Its multiplied by 2 because that is the width of the three triangles

=a. 2.64 for left endpoint