Mean Value Theorem For Integrals
Mean Value Theorem For Integrals

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Problems 10: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval:
f(x) = 5x – 4; [4,4]
g(x) = 3x^2 – 2; [0,2]
h(x) = x^3; [1,3]
k(x) = e^x; [-1,1]
Problems 11-16: Use a calculator and the Mean Value Theorem for Integrals to evaluate each of the following:
11. Compute the average value of the function f(t) = tcos(t) on the interval (0,10].
On a winter day in San Francisco, the temperature in Â°F at different hours after 1pm can be modeled by the function T(t) = 14sin(t). Find the average temperature during the period from 9am to 1pm.

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13. Use the average value of a function on an interval to solve the following: @ f(x)dx b-a Find the average value of f (x) = sinx on the interval [0,7].b. Find the values of c guaranteed by the Mean Value Theorem for integrals for f(x) on the interval.14, Write a definite integral that yields the area of the region: (Do not evaluate) f(x) = 6 – 3×5 3 f 2+++x 2 3 4 5C2-15. Find F’ (x).sinxFlx) =Vi dt

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12. Complete the following:(a) Find the average value of f (x) = Vx over the interval [1,4] (b) Let g(x) x2 _ At what value of c in the interval [0,4] does the value of g (c) equal the average value of g over the interval? 13. Evaluate the following using the Substitution Rule_ 1+6x (a) dx (d) sin? (x) cos(x) dx Vz +x+3x2Vx dx(b)(e)x(1 + 3×2)* dxx3(c)cos(x) sin(x) dxdx 2×4 _ 1

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Please help! ASAP1. If the integral from 1 to 6 of f of x, dx equals negative 10 and the integral from 3 to 6 of f of x, dx equals negative 8, then what is the value of integral from 1 to 3 of f of x, dx?A. 2B. -2C. -18D. 122. Use geometry to evaluate the integral from 0 to 6 of the function f of x, dx for f of x equals 4 for x less than or equal to 6 and equals the quantity 10 minus x for x greater than 6. (THIS IS THE ONE I NEED THE MOST HELP ON!!)A. 4B. 8C. 16 D. 24Thank you in advance! I really appreciate it 🙂

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