Find the average value of the function $f ( x ) = \sin 3 x \text { on the interval } \left[ 0 , \frac { \pi } { 3 } \right]$
A)1
B) $\frac { 3 } { 2 }$
C)2
D)6
E) $\frac { 1 } { \pi }$
F) $\frac { 2 } { \pi }$
G)0
H) $\frac { 5 } { 2 \pi }$

Question

Find the average value of the function $f ( x ) = \sin 3 x \text { on the interval } \left[ 0 , \frac { \pi } { 3 } \right]$ 
A)1
B) $\frac { 3 } { 2 }$ 
C)2
D)6
E) $\frac { 1 } { \pi }$ 
F) $\frac { 2 } { \pi }$ 
G)0
H) $\frac { 5 } { 2 \pi }$

Quizplus · Accepted Answer

The average value of a function $f(x)$ on an interval $[a,b]$ is given by $$\frac{1}{b-a}\int_a^b f(x) \ dx$$So, the average value of $f(x) = \sin 3x$ on the interval $[0, \frac{\pi}{3}]$ is$$\frac{1}{\frac{\pi}{3}-0}\int_0^{\frac{\pi}{3}} \sin 3x \ dx = \frac{3}{\pi}\left[-\frac{1}{3}\cos 3x\right]_0^{\frac{\pi}{3}} = \frac{2}{\pi}$$

Find the Average Value of the Function f(x)=sin⁡3x on the interval [0,π3]f ( x ) = \sin 3 x \text { on the interval } \left[ 0 , \frac { \pi } { 3 } \right]f(x)=sin3x on the interval [0,3π​]

Find the Average Value of the Function $f ( x ) = \sin 3 x \text { on the interval } \left[ 0 , \frac { \pi } { 3 } \right]$