What is the integral from pi/6 to pi/3 of cos(x) ?

The integral from pi/6 to pi/3 of cos(x) is (sqrt(3)-1)/2

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integral from pi/6 to pi/3 of cos(x)

\int_{\frac{π}{6}}^{\frac{π}{3}} cos (x) d x

\frac{3 - 1}{2}

Decimal

0.36602 \dots

Solution steps

\int_{\frac{π}{6}}^{\frac{π}{3}} cos (x) d x

Use the common integral:

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

= [sin (x)]_{\frac{π}{6}}^{\frac{π}{3}}

Compute the boundaries:

\frac{3}{2} - \frac{1}{2}

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

Simplify

= \frac{3 - 1}{2}

What is the integral from pi/6 to pi/3 of cos(x) ?
The integral from pi/6 to pi/3 of cos(x) is (sqrt(3)-1)/2