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

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

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integral from pi/4 to pi/2 of sin(t)

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

\frac{1}{2}

Decimal

0.70710 \dots

Solution steps

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

Use the common integral:

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

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

Compute the boundaries:

\frac{1}{2}

= \frac{1}{2}

\int_{0}^{\frac{π}{2}} 1 - cos (x) d x

\int_{0}^{1} 4 x^{3} ln (x) d x

\int_{1}^{4} x^{2} + 5 d x

\int_{- 2}^{3} e^{- t} d t

\int_{0}^{2} x^{2} + 3 x d x

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