Question

Math

Posted 5 months ago

`What is the average value of $-x^{2}+3$ on the interval $[0,6] ?$`

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Answer from Sia

Posted 5 months ago

Solution by Steps

step 1

Calculate the definite integral of the function $-x^2 + 3$ from 0 to 6

step 2

The result of the integral is $-54$

step 3

Divide the result of the integral by the length of the interval, which is 6, to find the average value

step 4

The average value is $-54 \div 6 = -9$

Answer

The average value of $-x^{2}+3$ on the interval $[0,6]$ is $-9$.

Key Concept

Average Value of a Function

Explanation

The average value of a continuous function $f(x)$ on the interval $[a,b]$ is given by $\frac{1}{b-a}\int_{a}^{b} f(x) dx$.

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