evaluate the definite integral by interpreting it in terms of signed area.

Question

𝑓(𝑥)={ 2 if 4 ≤ x < 10

-5 if 10 ≤ x ≤ 16

a) evaluate the definite integral by interpreting it in terms of signed area.

∫16 f(x) d(x)

4

b) find the average value of f(x) over the interval [4,16]

Answer 1

The integral from 4 to 10 is 6*2 = 12

The integral from 10 to 16 is 6*(-5) = -30

I think I will leave it to you to decide how to use this information because the question is not really clear.