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

The integral from x/2 to x of-sin(x) is cos(x)-cos(x/2)

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integral from x/2 to x of-sin(x)

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

cos (x) - cos (\frac{x}{2})

Solution steps

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

Take the constant out:

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

= - \int_{\frac{x}{2}}^{x} sin (x) d x

Use the common integral:

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

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

Compute the boundaries:

- cos (x) + cos (\frac{x}{2})

= - (- cos (x) + cos (\frac{x}{2}))

Simplify

= cos (x) - cos (\frac{x}{2})

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What is the integral from x/2 to x of-sin(x) ?
The integral from x/2 to x of-sin(x) is cos(x)-cos(x/2)