# Thread: More Definite Intergration questions

1. ## More Definite Intergration questions

Hi

I would like to know how would i evaluate the following:

1)$\displaystyle \int_0^\frac{\pi}{3}tanx$ dx

P.S

2. Just in case a picture helps...

$\displaystyle \int \tan x\ dx$ is a standard integral. Differentiate to confirm that you've remembered it right. Again, just in case a picture helps...

... where

... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

Edit: oops, thanks Captain Black - of course

$\displaystyle -\ln|\cos x|$

is better and easier.

_________________________________________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

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3. Originally Posted by Paymemoney
Hi

I would like to know how would i evaluate the following:

1)$\displaystyle \int_0^\frac{\pi}{3}tanx$ dx

P.S
You should be able to recognise the integrand as a derivative:

$\displaystyle \tan(x)=\frac{\sin(x)}{\cos(x)}=-\frac{d}{dx}\ln(|\cos(x)|)$

Then the fundamental theorem of calculus will allow you to finish.

CB