Evaluate the following integral. \int_{0}^{\frac{\pi}{4}}3\sec^{2}xdx

Evaluate the following integral.
${\int }_{0}^{\frac{\pi }{4}}3{\mathrm{sec}}^{2}xdx$
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2abehn
Step 1: Given that
Evaluate the following integral.
${\int }_{0}^{\frac{\pi }{4}}3{\mathrm{sec}}^{2}xdx$
Step 2: Formula Used
$\int {\mathrm{sec}}^{2}xdx=\mathrm{tan}x+C$
Step 3: Solving the Integral
We have,
${\int }_{0}^{\frac{\pi }{4}}3{\mathrm{sec}}^{2}xdx=3{\left[\mathrm{tan}x\right]}_{0}^{\frac{\pi }{4}}$
$=3\left[\mathrm{tan}\left(\frac{\pi }{4}\right)-\mathrm{tan}\left(0\right)\right]$
=3(1)
=3