CPM Homework Help : CALC3RD Problem 9-14

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9-14.

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

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

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

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

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

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

Hint:

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

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

More Help:

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

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