What is the integral from 0 to pi/6 of 6sec^2(x) ?

The integral from 0 to pi/6 of 6sec^2(x) is 2sqrt(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to pi/6 of 6sec^2(x)

\int_{0}^{\frac{π}{6}} 6 sec^{2} (x) d x

23

Decimal

3.46410 \dots

Solution steps

\int_{0}^{\frac{π}{6}} 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_{0}^{\frac{π}{6}} sec^{2} (x) d x

Use the common integral:

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

= 6 [tan (x)]_{0}^{\frac{π}{6}}

Compute the boundaries:

\frac{1}{3}

= 6 \cdot \frac{1}{3}

Simplify

= 23

What is the integral from 0 to pi/6 of 6sec^2(x) ?
The integral from 0 to pi/6 of 6sec^2(x) is 2sqrt(3)