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

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

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

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

- 1 + \frac{1}{2}

Decimal

- 0.29289 \dots

Solution steps

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \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})

Simplify

= - 1 + \frac{1}{2}

\int_{0}^{1} y^{2} (1 - y^{2}) d y

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