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

Question

banganX 2021-10-26 Answered

Evaluate the following integral.

\int_{0}^{\frac{π}{4}} 3 \sec^{2} x d x

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Expert Answer

2abehn

Answered 2021-10-27 Author has 88 answers

Step 1: Given that
Evaluate the following integral.

\int_{0}^{\frac{π}{4}} 3 \sec^{2} x d x

Step 2: Formula Used

\int \sec^{2} x d x = \tan x + C

Step 3: Solving the Integral
We have,

\int_{0}^{\frac{π}{4}} 3 \sec^{2} x d x = 3 {[\tan x]}_{0}^{\frac{π}{4}}

= 3 [\tan (\frac{π}{4}) - \tan (0)]

=3(1)
=3

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