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...

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

f_{av = 1/(20 - 10)∫10}²⁰ _{f(x)dx ≈ 1/10L4 = 1/10[-2·2 + (-5)·3 + (-9)·4 + (-12)·1] = - 6.700}