What is the integral from-pi/8 to pi/(12) of cos(2x) ?

The integral from-pi/8 to pi/(12) of cos(2x) is (1+sqrt(2))/4

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integral from-pi/8 to pi/(12) of cos(2x)

\int_{- \frac{π}{8}}^{\frac{π}{12}} cos (2 x) d x

\frac{1 + 2}{4}

Decimal

0.60355 \dots

Solution steps

\int_{- \frac{π}{8}}^{\frac{π}{12}} cos (2 x) d x

Apply u-substitution

= \int_{- \frac{π}{4}}^{\frac{π}{6}} cos (u) \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{- \frac{π}{4}}^{\frac{π}{6}} cos (u) d u

Use the common integral:

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

= \frac{1}{2} [sin (u)]_{- \frac{π}{4}}^{\frac{π}{6}}

Compute the boundaries:

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

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

Simplify

= \frac{1 + 2}{4}

What is the integral from-pi/8 to pi/(12) of cos(2x) ?
The integral from-pi/8 to pi/(12) of cos(2x) is (1+sqrt(2))/4