### Home > APCALC > Chapter 9 > Lesson 9.1.1 > Problem9-14

9-14.

Multiple Choice: What is the average value of $y=x\sqrt{x^2+1}$ on the interval $[0, 2]$?

1. $\frac { 5 } { 4 }\sqrt { 5 }$

1. $\frac { 5 } { 6 }\sqrt { 5 }$

1. $\frac { 1 } { 6 } ( 5 \sqrt { 5 } - 1 )$

1. $\frac { 1 } { 4 } ( 5 \sqrt { 5 } - 1 )$

1. $\frac { 1 } { 3 } ( 5 \sqrt { 5 } - 1 )$

The average value of a function is computed using the formula:

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

To integrate, use substitution. Let $u = x^2 + 1$.