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

The integral from pi/6 to pi/2 of 2sin(x) is square root of 3

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integral from pi/6 to pi/2 of 2sin(x)

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

3

Decimal

1.73205 \dots

Solution steps

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

Take the constant out:

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

= 2 \cdot \int_{\frac{π}{6}}^{\frac{π}{2}} sin (x) d x

Use the common integral:

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

= 2 [- cos (x)]_{\frac{π}{6}}^{\frac{π}{2}}

Compute the boundaries:

\frac{3}{2}

= 2 \cdot \frac{3}{2}

Simplify

= 3

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What is the integral from pi/6 to pi/2 of 2sin(x) ?
The integral from pi/6 to pi/2 of 2sin(x) is square root of 3