1. ## Definite integral problem

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

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

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

$\displaystyle \displaystyle\int^{\pi}_0 \sec^2 \left(\frac{t}{3}\right) dt$
Note that $\displaystyle \frac{d [\tan (a t)]}{dt} = a \, \sec^2 (at)$.

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

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

4. Thank you so much, I've got it now!