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.)
 👍
 👎
 👁
 ℹ️
 🚩
1 answer

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

ba
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. 👍
 👎
 ℹ️
 🚩
👤oobleck
Answer this Question
Related Questions

Calculus
Let f be the function defined by f(x)=2sinx+cosx ? The average rate of change of f over the interval [0,b] is 0.05, where b>0 . Which of the following is an equation that could be used to find the value of b? A) f(b)=0.05 B) f(b)−f(0)=0.05 C:

Calculus
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 Trapezoidal Sum Approximation, using the intervals between those given points. x 10;12;15;19;20 f(x)

Math
Determine the value of 'a' so that the average rate of change of the function h(x)=x^2+3x+2 on the interval 3

science
A ball rolling down an incline travels 6.0 cm in the first 0.25 econds, and 24 cm in the first 0.50 seconds. Find: a)The average speed for the first quarter second time interval B) The average speed for the second time interval C) Find its acceleration

Algebra
Find the average rate of change of f(x)=6x²−3 on the interval [2,a]. Your answer will be an expression involving a What I did so far: I found f(2) which is 21 and that would make the function (2,21) Then, I found f(a) which is 6a^23 and that would make

calculus
g(t)=2+cos t; [0,pi] Can you help me find the average rate of change of the function over the given interval?

Calculus
The position (feet traveled) of a car is given by the equation s(t)=(1/4)t^2+1 find the time when the car is going the same speed as its average speed over the interval 0 to 10 seconds t=0 t=2.5 t=5 t=10 Never I think it's either t=5 or t=2.5? The end

Physics
A mouse travels along a straight line; its distance from the origin at any time is given by the equation. x= (8.1 cm * s^1)t(2.7cm * s^2)t^2 A) Find the average velocity of the mouse in the interval from t= 0 to t= 1.0 . value=?; unit= ? B)Find the

Physics
A Honda Civic travels in a straight line along a road. Its distance x from a stop sign is given as a function of time t by the equation x(t)= α t2− β t3, where α = 1.40m/s2 and β = 5.05×10−2m/s3 A) What is the average velocity of the car for the

math
Find the average cost function C associated with the following total cost function C. C(x) = 0.000007x3  0.06x2 + 110x + 76000 C(x) = ?? (a) What is the marginal average cost function C' ? C'(x) = ?? (b) Compute the following values. (Round your answers

Math  PreCalc (12th Grade)
The function f(x) = 2x + 1 is defined over the interval [2, 5]. If the interval is divided into n equal parts, what is the value of the function at the right endpoint of the kth rectangle? A) 2+3k/n B) 4+3k/n C) 4+6k/n D) 5+6k/n E) 5+3k/n

Mathematics
What is the average rate of change of the function below on the interval [4,3]? f(x)= 1/x^3

Calculus
Consider f(x)=x^22x3 (a). Find the average value of f(x) on the interval [0,3] (b). Find the value(s) of C in [0,3] guaranteed by the Mean Value Theorem for Integrals. Any help is appreciated!

Physics
An athlete starts at point A and runs at a constant speed of 5.40 m/s around a round track 250 m in diameter. Find the x component of this runner's average velocity between points A and B. (answer is 3.44 m/s) Find the y component of this runner's average

calculus
h(t)=cot t a.) [pi/4,3pi/4] b.) [pi/6,pi/2] Find the average rate of change of the function over the give n interval and intervals. Please show step by step instructions. Thanks

Physics
At an air show, a jet plane has velocity components vx = 695 km/h and vy = 440 km/h at time 4.85s and vx= 933km/h and vy = 465 km/h at time 7.12 s. For this time interval, find (a) the x and y components of the plane’s average acceleration and (b) the

calculus
Consider the given function and the given interval. f(x) = 4 sin x − 2 sin 2x, [0, π] (a) Find the average value fave of f on the given interval. fave = (b) Find c such that fave = f(c). (Round your answers to three decimal places.) c = (smaller value)

Calculus AP Exam review explanation pls
1) The average value of the function g(x) = 3^cos x on the closed interval [ − pi , 0 ] is: 2)The change in the momentum of an object (Δ p) is given by the force, F, acting on the object multiplied by the time interval that the force was acting: Δ p =

calculus
Consider the given function and the given interval. f(x) = 10 sin(x) − 5 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.)

mathematics
The function y=f(x)y=f(x) is graphed below. What is the average rate of change of the function f(x)f(x) on the interval 8\le x \le 8−8≤x≤8?
Still need help?
You can ask a new question or browse existing questions.