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

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

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

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

\frac{- 1 + 3}{2}

Decimal

0.36602 \dots

Solution steps

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

Use the common integral:

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

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

Compute the boundaries:

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

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

Simplify

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

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