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

The integral from pi/4 to pi/2 of cos(x) is 1-1/(sqrt(2))

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integral from pi/4 to pi/2 of cos(x)

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

1 - \frac{1}{2}

Decimal

0.29289 \dots

Solution steps

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

Use the common integral:

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

= [sin (x)]_{\frac{π}{4}}^{\frac{π}{2}}

Compute the boundaries:

1 - \frac{1}{2}

= 1 - \frac{1}{2}

What is the integral from pi/4 to pi/2 of cos(x) ?
The integral from pi/4 to pi/2 of cos(x) is 1-1/(sqrt(2))