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)

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

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

23

Decimal Notation

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

2 y^{^{''}} + 4 y^{^{'}} - 7 y = 7 cos (2 x)

\int 1 + x d x

f (x) = e^{3 x}, at x = \frac{1}{3} ln (5)

\frac{d}{d x} (sin (x) ln (2 x))

\frac{d}{d x} (x \cdot e^{- 3 x})

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)