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

The integral from pi/4 to pi/2 of sin(θ) is 1/(sqrt(2))

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integral from pi/4 to pi/2 of sin(θ)

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

\frac{1}{2}

Decimal Notation

0.70710 \dots

Solution steps

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

Use the common integral:

\int sin (θ) d θ = - cos (θ)

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

Compute the boundaries:

\frac{1}{2}

= \frac{1}{2}

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What is the integral from pi/4 to pi/2 of sin(θ) ?
The integral from pi/4 to pi/2 of sin(θ) is 1/(sqrt(2))