What is the integral from x/4 to x/2 of sin(x) ?

The integral from x/4 to x/2 of sin(x) is -cos(x/2)+cos(x/4)

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integral from x/4 to x/2 of sin(x)

\int_{\frac{x}{4}}^{\frac{x}{2}} sin (x) d x

- cos (\frac{x}{2}) + cos (\frac{x}{4})

Solution steps

\int_{\frac{x}{4}}^{\frac{x}{2}} sin (x) d x

Use the common integral:

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

= [- cos (x)]_{\frac{x}{4}}^{\frac{x}{2}}

Compute the boundaries:

- cos (\frac{x}{2}) + cos (\frac{x}{4})

= - cos (\frac{x}{2}) + cos (\frac{x}{4})

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What is the integral from x/4 to x/2 of sin(x) ?
The integral from x/4 to x/2 of sin(x) is -cos(x/2)+cos(x/4)