Knowee
Questions
Features
Study Tools

Find the average value gave of the function g on the given interval.g(x) = 5 cos(x),   − 𝜋2, 𝜋2

Question

Find the average value of the function

g(x) = 5 cos(x) on the interval ( [−\frac{\pi}{2}, \frac{\pi}{2}] \

🧐 Not the exact question you are looking for?Go ask a question

Solution

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 π/2 [5cos(x) dx]

The integral of cos(x) is sin(x), so we have:

2/π * [5sin(x)] from -π/2 to π/2

Evaluating this gives:

2/π * [5sin(π/2) - 5sin(-π/2)]

Since sin(π/2) = 1 and sin(-π/2) = -1, this further simplifies to:

2/π * [51 - 5(-1)] = 2/π * [5 + 5] = 2/π * 10 = 20/π

So, the average value of the function g(x) = 5cos(x) on the interval [-π/2, π/2] is 20/π.

This problem has been solved

Similar Questions

Find the average rate of change of g(x)=−5x2−1𝑔(𝑥)=-5𝑥2-1 on the interval [−1,3][-1,3] .

If 𝑓(𝑔(𝑥))=cos(5𝑥+4), find the functions 𝑓(𝑥) and 𝑔(𝑥).Note: there may be more than one solution, but do not use the trivial solution 𝑔(𝑥)=𝑥.𝑓(𝑥)= 𝑔(𝑥)=

Write a cosine function that has a midline of y, equals, 5, commay=5, an amplitude of 2 and a period of start fraction, pi, divided by, 2, end fraction 2π​ .

Determine the average rate of change of 𝑦 in the function 𝑦=2𝑥3+7𝑥2+2𝑥−3 over the interval [3, 5].

Instructions: Find the value by evaluating the function. Do not include any spaces in your answer. Function: g(x)=x2−5𝑔(𝑥)=𝑥2−5Find: g(0)𝑔(0)Solution:

1/1

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.