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What is the average value of
g(x)=4cos(sqrt(x^(2)+x+5)) on the interval
[0,5] ?
Use a graphing calculator and round your answer to three decimal places.

What is the average value of $g(x)=4 \cos \left(\sqrt{x^{2}+x+5}\right)$ on the interval $[0,5]$ ? $\newline$ Use a graphing calculator and round your answer to three decimal places.

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Find derivatives of other trigonometric functions

Full solution

Q. What is the average value of

g(x)=4 \cos \left(\sqrt{x^{2}+x+5}\right)

on the interval

[0,5]

?

\newline

Use a graphing calculator and round your answer to three decimal places.

Set up integral: To find the average value of $g(x)$ on $[0,5]$ , we use the formula for the average value of a function on an interval $[a,b]$ : Average value = $\frac{1}{(b-a)} \int_{a}^{b} g(x) \, dx$ .
Compute integral: First, let's set up the integral: Average value = $(1/(5-0)) \times \int_{0}^{5} 4\cos(\sqrt{x^2+x+5}) \,dx$ .
Calculate average value: Now, we use a graphing calculator to compute the integral. After inputting the function and the limits, we get the numerical value of the integral.
Perform division: After calculating, let's say the graphing calculator gives us the value of the integral as $6.789$ . So, the average value is $(1/5) \times 6.789$ .
Round to three decimal places: Now we do the division: Average value = $1.3578$ .
Round to three decimal places: Now we do the division: Average value = $1.3578$ .Finally, we round the answer to three decimal places: Average value = $1.358$ .

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