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

The integral from 0 to pi/6 of 2cos(x) is 1

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

\int_{0}^{\frac{π}{6}} 2 cos (x) d x

1

Solution steps

\int_{0}^{\frac{π}{6}} 2 cos (x) d x

Take the constant out:

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

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

Use the common integral:

\int cos (x) d x = sin (x)

= 2 [sin (x)]_{0}^{\frac{π}{6}}

Compute the boundaries:

\frac{1}{2}

= 2 \cdot \frac{1}{2}

Simplify

= 1

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What is the integral from 0 to pi/6 of 2cos(x) ?
The integral from 0 to pi/6 of 2cos(x) is 1