Evaluate the following integral.

${\int}_{0}^{\frac{\pi}{4}}3{\mathrm{sec}}^{2}xdx$

banganX
2021-10-26
Answered

Evaluate the following integral.

${\int}_{0}^{\frac{\pi}{4}}3{\mathrm{sec}}^{2}xdx$

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2abehn

Answered 2021-10-27
Author has **88** answers

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,

$\int}_{0}^{\frac{\pi}{4}}3{\mathrm{sec}}^{2}xdx=3{\left[\mathrm{tan}x\right]}_{0}^{\frac{\pi}{4}$

$=3[\mathrm{tan}\left(\frac{\pi}{4}\right)-\mathrm{tan}\left(0\right)]$

=3(1)

=3

Evaluate the following integral.

Step 2: Formula Used

Step 3: Solving the Integral

We have,

=3(1)

=3

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