Could someone show me the steps for a problem like this? I missed a class and you'd be saving my life.

$\displaystyle \displaystyle\int^{\pi}_0 \sec^2 \left(\frac{t}{3} \right) dt$

Printable View

- Jan 19th 2009, 12:32 PMDana_ScullyDefinite integral problem
Could someone show me the steps for a problem like this? I missed a class and you'd be saving my life.

$\displaystyle \displaystyle\int^{\pi}_0 \sec^2 \left(\frac{t}{3} \right) dt$ - Jan 19th 2009, 12:37 PMmr fantastic
- Jan 19th 2009, 12:39 PMJester
Make the substitution $\displaystyle u = \frac{t}{3}$ so $\displaystyle du = \frac{dt}{3}$. New limits of integration $\displaystyle t = 0 \; \Rightarrow \; u = 0, \; \; t = \pi \; \Rightarrow \; u = \frac{ \pi }{3}$

New problem

$\displaystyle 3 \int_0^{\frac{\pi}{3}} \sec^2 u \,du$

You should recognize the antiderivative for this. - Jan 19th 2009, 12:58 PMDana_Scully
Thank you so much, I've got it now!