What is the integral from 0 to pi/4 of (2sec^2(x)) ?

The integral from 0 to pi/4 of (2sec^2(x)) is 2

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integral from 0 to pi/4 of (2sec^2(x))

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

2

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{0}^{\frac{π}{4}} sec^{2} (x) d x

Use the common integral:

\int sec^{2} (x) d x = tan (x)

= 2 [tan (x)]_{0}^{\frac{π}{4}}

Compute the boundaries:

1

= 2 \cdot 1

Simplify

= 2

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What is the integral from 0 to pi/4 of (2sec^2(x)) ?
The integral from 0 to pi/4 of (2sec^2(x)) is 2