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

The integral from pi/6 to pi/4 of cos(2x) is (2-sqrt(3))/4

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

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

\frac{2 - 3}{4}

Decimal Notation

0.06698 \dots

Solution steps

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

Apply u-substitution

: \int_{\frac{π}{3}}^{\frac{π}{2}} cos (u) \frac{1}{2} d u

= \int_{\frac{π}{3}}^{\frac{π}{2}} 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}{3}}^{\frac{π}{2}} cos (u) d u

Use the common integral:

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

= \frac{1}{2} [sin (u)]_{\frac{π}{3}}^{\frac{π}{2}}

Compute the boundaries:

1 - \frac{3}{2}

= \frac{1}{2} (1 - \frac{3}{2})

Simplify

= \frac{2 - 3}{4}

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What is the integral from pi/6 to pi/4 of cos(2x) ?
The integral from pi/6 to pi/4 of cos(2x) is (2-sqrt(3))/4