What is the integral from-pi/4 to pi/4 of 6sec^2(x) ?

The integral from-pi/4 to pi/4 of 6sec^2(x) is 12

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integral from-pi/4 to pi/4 of 6sec^2(x)

\int_{- \frac{π}{4}}^{\frac{π}{4}} 6 sec^{2} (x) d x

12

Solution steps

\int_{- \frac{π}{4}}^{\frac{π}{4}} 6 sec^{2} (x) d x

Take the constant out:

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

= 6 \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)

= 6 [tan (x)]_{- \frac{π}{4}}^{\frac{π}{4}}

Compute the boundaries:

2

= 6 \cdot 2

Simplify

= 12

\int_{0}^{1} \frac{x}{1 + 4 x ^{2}} d x

\int_{0}^{\infty} \frac{1}{x + 3} d x

\int_{1}^{4} (2 - 9 x - 4 x^{2}) d x

\int_{0}^{1} x e^{- 9 x} d x

\int_{0}^{2} sin (t^{2}) d t

What is the integral from-pi/4 to pi/4 of 6sec^2(x) ?
The integral from-pi/4 to pi/4 of 6sec^2(x) is 12