Question

Please help.
Find f(antiderivative) . f'(t) =6 cos t + sec^2t, -pi/2pi/2, f(pi/3)=4

Answer 1

\[f'(t)=6\cos t+\sec^2t~~\Rightarrow~~\int f'(t)~dt=\int(6\cos t+\sec^2t)~dt\]
Integrating gives
\[f(t)=6\sin t+\tan t+C\]
You can find the value of \(C\) using the given initial value, \(f\left(\dfrac{\pi}{3}\right)=4\):
\[4=6\sin\frac{\pi}{3}+\tan\frac{\pi}{3}+C\]