calculus

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.)

  1. 👍
  2. 👎
  3. 👁
  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.

    1. 👍
    2. 👎
    👤
    oobleck

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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)

  2. 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?

  3. 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

  4. calculus (rate of change)

    consider the function f(x)=x^2-6x+12 a. find the average rate of change over the interval [-1,3] b. use the definition of the derivative to find f prime(x) c. find the instantaneous rate of change at the point where x=3 d. find

  1. Mathematics

    Examine the following graph of the linear function f(x)=2x+1 and the quadratic function g(x)=−116(x+3)2+6. Graph of g of x is a downward opening parabola that passes through points (negative 4, 5), (negative 3, 6), & (1, 5). f

  2. 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

  3. AP CALC

    1. Let f be a twice-differentiable function such that f (2) = 8 and f (4) = 5. Which of the following must be true for the function f on the interval 2 ≤ x ≤ 4. I. The average value of f is 6.5 II. The average rate of change

  4. Calculus

    1. 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

  1. Urgent!!! Physics

    At an air show, a jet plane has velocity components Vx = 625 and Vy = 415 at time 3.85s and Vx = 838 and Vy = 365 at time 6.52s . A. For this time interval, find the x component of the plane's average acceleration in km/h2. B. For

  2. physics

    In this problem you will determine the average velocity of a moving object from the graph of its position as a function of time . A traveling object might move at different speeds and in different directions during an interval of

  3. Calculus

    Find the average value g-ave of the function g on the given interval. g(x) = 6∛x [27, 125]

  4. 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

You can view more similar questions or ask a new question.