Find the average value of the function $f ( x ) = \frac { 2 x } { 2 x + 3 }$ over the interval [2, 6]. Round your answer to two decimal places.
A) 0.71
B) 2.86
C) 1.29
D) 1.71

Question

Quizplus · Accepted Answer

The average value of a function $f(x)$ over an interval [a, b] is given by the formula:$$\frac{1}{b-a}\int_a^b f(x) dx$$So, for the given function and interval, we have:$$\frac{1}{6-2}\int_2^6 \frac{2x}{2x+3} dx$$$$=\frac{1}{4}\int_2^6 \frac{2x}{2x+3} dx$$$$=\frac{1}{4}\ln|2x+3| \bigg|_2^6$$$$=\frac{1}{4}(\ln 15 - \ln 7)$$$$=\frac{1}{4}\ln \frac{15}{7}$$$$\approx 0.71$$Therefore, the average value of the function over the interval [2, 6] is approximately 0.71.

Find the Average Value of the Function f(x)=2x2x+3f ( x ) = \frac { 2 x } { 2 x + 3 }f(x)=2x+32x​

Find the Average Value of the Function $f ( x ) = \frac { 2 x } { 2 x + 3 }$