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

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

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

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

4

Solution steps

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

Use the common integral:

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

= 2 [tan (x)]_{- \frac{π}{4}}^{\frac{π}{4}}

Compute the boundaries:

2

= 2 \cdot 2

Simplify

= 4

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