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

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

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

\int_{0}^{\frac{π}{6}} 3 sec^{2} (x) d x

3

Decimal Notation

1.73205 \dots

Solution steps

\int_{0}^{\frac{π}{6}} 3 sec^{2} (x) d x

Take the constant out:

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

= 3 \cdot \int_{0}^{\frac{π}{6}} sec^{2} (x) d x

Use the common integral:

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

= 3 [tan (x)]_{0}^{\frac{π}{6}}

Compute the boundaries:

\frac{1}{3}

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

Simplify

= 3

\int cos^{3} (\frac{1}{3}) x d x

\frac{d y}{d x} + \frac{1}{x} y = 3 cos (2 x)

\int \frac{1}{1 + 7 x} d x

\frac{\partial}{\partial x} (x^{2} + y^{2} - 2)

\frac{\partial}{\partial x} (ln (6 y e^{x y}))

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