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

The integral from-pi/4 to-pi/6 of 2cos(x) is -1+sqrt(2)

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

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

- 1 + 2

Decimal Notation

0.41421 \dots

Solution steps

\int_{- \frac{π}{4}}^{- \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_{- \frac{π}{4}}^{- \frac{π}{6}} cos (x) d x

Use the common integral:

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

= 2 [sin (x)]_{- \frac{π}{4}}^{- \frac{π}{6}}

Compute the boundaries:

- \frac{1}{2} + \frac{1}{2}

= 2 (- \frac{1}{2} + \frac{1}{2})

Simplify

= - 1 + 2

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What is the integral from-pi/4 to-pi/6 of 2cos(x) ?
The integral from-pi/4 to-pi/6 of 2cos(x) is -1+sqrt(2)