We can use the following common integral for part (a):
[tex]\int\sec^2(t)dt=\tan(t)[/tex]
Since this is a definite integral, we have
[tex]\int_{\frac{\pi}{4}}^x\sec^2(t)=[\tan(t)]_{\frac{\pi}{4}}^x[/tex]
So we have:
[tex]\begin{gathered} \tan(x)-\tan(\frac{\pi}{4}) \\ \end{gathered}[/tex]
Evaluating the second tangent, we get
[tex]\begin{gathered} \tan{\frac{\pi}{4}}=1 \\ \\ \tan{(x})-1 \end{gathered}[/tex]
The correct final answer will be tan(x)-1.
