Question

Evaluate the definite integral.

Answer 1

\[\int\limits_{0}^{\pi} \sec ^{2}(t/3)dt\]

Answer 2

For the integrand substitute:
\[u=t/3 \]
\[du=1/3dt\]
\[3\int\limits_{0}^{\pi}\sec^2(u)du\]
integral of that is
\[3\tan(u) + C\]
Re-insert u=t/3
so \[3\tan(t/3)\] from 0 tp pi
3tan(pi/3)-3tan(0/3) = \[3\sqrt{3}\]

Answer 3

I was just missing the 3 in front of the root 3 thanks