What is the integral from 1/2 pi to pi of 2sin(x) ?

The integral from 1/2 pi to pi of 2sin(x) is 2

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integral from 1/2 pi to pi of 2sin(x)

\int_{\frac{1}{2} π}^{π} 2 sin (x) d x

2

Solution steps

\int_{\frac{1}{2} π}^{π} 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{1}{2} π}^{π} sin (x) d x

Use the common integral:

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

= 2 [- cos (x)]_{\frac{1}{2} π}^{π}

Multiply

\frac{1}{2} π : \frac{π}{2}

= 2 [- cos (x)]_{\frac{π}{2}}^{π}

Compute the boundaries:

1

= 2 \cdot 1

Simplify

= 2

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What is the integral from 1/2 pi to pi of 2sin(x) ?
The integral from 1/2 pi to pi of 2sin(x) is 2