Find the average value gave of the function g on the given interval.g(x) = 5 cos(x), − 𝜋2, 𝜋2
Question
Solution 1
The average value of a function on the interval [a, b] is given by the formula:
1/(b - a) * ∫ from a to b [f(x) dx]
Here, our function g(x) = 5cos(x) and the interval is [-π/2, π/2].
So, we need to find:
1/(π - (-π/2)) * ∫ from -π/2 to π/2 [5cos(x) dx]
This simplifies to:
2/π * ∫ from -π/2 to Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
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