Find the average value of the function over the given interval.
-f(x) = x + 2 on [-3, 3]
A) $\frac { 7 } { 6 }$
B) 7
C) $\frac { 7 } { 2 }$
D) 21

Question

Find the average value of the function over the given interval.
-f(x) = x + 2 on [-3, 3] 
A) $\frac { 7 } { 6 }$
B) 7
C) $\frac { 7 } { 2 }$
D) 21

Quizplus · Accepted Answer

The formula for the average value of a function on an interval is:

$$\frac{1}{b-a}\int_a^b f(x) dx$$

In this case, $a=-3$, $b=3$, and $f(x)=x+2$. So, we have:

$$\frac{1}{3-(-3)}\int_{-3}^3 (x+2) dx = \frac{1}{6} \left[\frac{x^2}{2} + 2x \right]_{-3}^3 = \frac{1}{6} \left[ \frac{3^2}{2} + 2(3) - \frac{(-3)^2}{2} - 2(-3)\right] = \frac{1}{6} \left[ \frac{9}{2} + 6 + \frac{9}{2} + 6 \right] = \boxed{\frac{7}{2}}$$

Find the Average Value of the Function Over the Given 76\frac { 7 } { 6 }67​

Find the Average Value of the Function Over the Given $\frac { 7 } { 6 }$