Question

Evaluate the integral from 0 to pi/3 of (sinx+(sinx)(tanx)^2)/(secx)^2

Answer 1

\[\int\limits_{0}^{\pi/3}\frac{ \sin (\theta)+\sin (\theta) \tan ^2(\theta) }{ \sec ^2(\theta) }\]

Answer 2

take sin theta common and 1+tan^2 theta=sec^2 theta

Answer 3

what do you mean by sin theta common?

Answer 4

\[\int\limits_{0}^{\frac{ \pi }{ 3 }}\frac{ \sin \theta \left( 1+\tan ^2\theta \right) }{ \sec ^2\theta }d\]

Answer 5

I am still confused. Did you do this?
\[\int\limits_{0}^{\pi/3}\frac{ \sin \theta}{ \sec ^2 \theta} + \int\limits_{0}^{\pi/3}\frac{ \sin \theta \tan^2 \theta }{ \sec^2 \theta } \]

Answer 6

\[\int\limits_{0}^{\frac{ \pi }{ 3 }}\frac{ \sin \theta \sec ^2\theta }{ \sec ^2\theta }d \theta =\int\limits_{0}^{\frac{ \pi }{ 3 }} \sin \theta d \theta =?\]

Answer 7

How did you get that first part?
\[\int\limits_{0}^{\pi/3} -\cos \theta\] is the answer to your question

Answer 8

OOOOOHHHH! I GET IT!