Question

1. Find the average value have of the function h on the given interval.
h(x) = 2 cos4(x) sin(x), [0, π]
2. Consider the given function and the given interval.
f(x) = 6 sin(x) − 3 sin(2x), [0, π]
(a) Find the average value fave of f on the given interval.
(b) Find c such that fave = f(c). (Round your answers to three decimal places.)
3. Find the numbers b such that the average value of
f(x) = 3 + 10x − 9x2
on the interval [0, b] is equal to 4.
4. In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function
T(t) = 48 + 19 sin

πt
12

.
Find the average temperature Tave during the period from 9 AM to 9 PM. (Round your answer to the nearest whole number.)

Answer 1

Recall that the average value of f(x) on the interval [a,b] is
∫[a,b] f(x) dx
--------------------
b-a

So,
#1.
(∫[0,π] 2 cos4x sinx dx)/π = -4 / 15π

#2. f(x) = 6 sin(x) − 3 sin(2x), [0, π]
avg value is 12/π
So, where is f(x) = 12/π ?

#3. f(x) = 3 + 10x - 9x^2
You want
(∫[0,b] f(x) dx)/4 = 4
(3x + 5x^2 - 3x^3)[0,b] = 4*4
3b + 5b^2 - 3b^3 = 16
b = -1.4724

#4. Fix your formatting so we can read the actual function.
Then apply the rules followed above.