The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Left Hand Sum...

Question

The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Left Hand Sum Approximation, using the intervals between those given points.



f(x)	-2	-5	-9	-12	-16

x 10 12 15 19 20

A	-9.250
B	-10.100
C	-7.550
D	-6.700

Answer 1

4

S = ∑f(x_i)Δx_i/(20-10) For left hand sum

_i=1

Δx₁=2

Δx₂=3

Δx₃=4

Δx₄=1

S = (1/10)[-2(2) - 5(3) - 9(4) - 12(1)]

= -67/10 = -6.7