Integral Calculus - Finding average value!!

Let f be a continuous function on [ -3 , 6 ],
the average value of f(x) on [ -3 , -1 ] is 5
the average value of f(x) on [ -1 , 2 ] is 4
the average value of f(x) on [ 2, 6 ] is 2

Let g(x) = 2 + f(x)
Find the average value of g(x) on [-3 , 6 ]

Answers

A. 17/3
B. 17/4
C. 16/3
D. 13/2
E. 13/3

Since the avg value of f(x) from -3 to -1 is 5 the integral is 10. The area from -1 to 2 is 12 and the area from 2 to 6 is 8

So the total area from -3 to 6 is 30

To find the avg value from -3 to 6 on g(x)

Integral of f(x) from -3 to 6 + Integral of 2 from -3 to 6
=30+18
=48

Average value=(1/9)(48) = 16/3

C

Good job MathNerd!! I like your thought process.

Report Abuse

All you have to is add 2 to each average vale for each interval. Then take the average valué.
So your set should be: (7+6+4)/3=17/3.