Finding the concavity of the integral of 1/(1+t²) from 0 to x²

[jhayes25]

Homework Statement

Not real good with the easy text stuff yet so ill give it a shot.

definite integral of (1/(1+t^2))dt from 0 to x^2
then find the interval for which the curve is concave upward.

I totally forgot how to integrate problems like this. It is some sort of substitution I know.

Help?

Would the integral of this involve a natural log?

 

[PowerIso]

What you have in your integral is arctan. Probably something you should memorize.

 

[Kurdt]

You'd need a trigonometric substitution for that integral. It works out quite neatly in the end.

Or recognise that the integrand is the derivative of arctan.