[SOLVED] Can't figure out integral with sqrt

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May 4th 2010, 07:15 AM
x3bnm

[SOLVED] Can't figure out integral with sqrt

I can't seem to figure out the following integration:

$<br /> \int_0^1 2\sqrt{1+t^2} dt = \left[2\left(\frac{t}{2}\sqrt{1+t^2} + \frac{1}{2}\ln\left(t+\sqrt{1+t^2}\right)\right)\r ight]_0^1<br />$

How do i reach the right side of equal sign?
Can anyone kindly tell what method is used for
the above integration?
May 4th 2010, 07:22 AM
shawsend

I think it's trig substitution. Let $t=\tan(\theta)$
May 4th 2010, 07:27 AM
x3bnm

You are absolutely right. How did i miss that? Thanks a lot for help.

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