What is the integral from-pi/3 to (5pi)/6 of sin(x) ?

The integral from-pi/3 to (5pi)/6 of sin(x) is (sqrt(3)+1)/2

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integral from-pi/3 to (5pi)/6 of sin(x)

\int_{- \frac{π}{3}}^{\frac{5 π}{6}} sin (x) d x

\frac{3 + 1}{2}

Decimal

1.36602 \dots

Solution steps

\int_{- \frac{π}{3}}^{\frac{5 π}{6}} sin (x) d x

Use the common integral:

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

= [- cos (x)]_{- \frac{π}{3}}^{\frac{5 π}{6}}

Compute the boundaries:

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

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

Simplify

= \frac{3 + 1}{2}

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What is the integral from-pi/3 to (5pi)/6 of sin(x) ?
The integral from-pi/3 to (5pi)/6 of sin(x) is (sqrt(3)+1)/2