# How do you find the average value of #f(x)=x/sqrt(x^2+1), 0<=x<=4#?

##### 2 Answers

The average value of

#### Explanation:

The average value of a continuous function

This now becomes a trig substitution problem. Let

Use the pythagorean identity

This is a known integral.

We know from our initial substitution that

Evaluate this using the 2nd fundamental theorem of calculus.

Hopefully this helps!

Alternative to get

#### Explanation:

Like HSBC244 said, The average value of a continuous function

Instead of doing a trig substitution like HSBC244, you can do a u substitution instead. Set

Note that the limits of integration changed because we were doing a u substitution. 0 became 1 because:

Similarly plugging in 4 became 17 because:

Now rewrite it so it's easier to integrate by treating the square root in the denominator:

This integral becomes

Take the 2 out and plug in 17 and 1. As you can see, this will give you the same answer as HSBC244's answer but does not require a trig substitution.