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Calculus Fave problems help!!!!?
1. Find the average value fave of the function f on the given interval.
f(x) = 14x − x^2, [0, 5]
2. Find the average value fave of the function f on the given interval.
f(x) = 3 sin(2x), [−π, π]
3. f(x) = 2 sq rt of x, [0, 25]
(a) Find the average value fave of f on the given interval.
(b) Find c such that fave = f(c). (Round your answer to three decimal places.)
3 Answers
- Mike GLv 74 years ago
1] A = Average value
A = (1/5)∫14x-x^2 dx [0,5]
A = (1/5)(7x^2-x^3/3) [0,5]
A = (1/5)[175-125/3]
A = 35-25/3 = 80/3
- 4 years ago
1.
Average value = 1/5 * integral from 0 to 5 of x(14x - x^2) dx = 85.417
2.
Average value = 1/(pi-(-pi))* integral from -pi to pi of x*3 sin(2x) = -1.5
3.Average value = 1/25* integral from 0 to 25 of x*2sqrtx = 100
b) f(c) = 100
2sqrt(x) = 100
x = 50^2 = 2500
