What is the integral from 5 to 4 of sin(x) ?

The integral from 5 to 4 of sin(x) is cos(5)-cos(4)

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integral from 5 to 4 of sin(x)

\int_{5}^{4} sin (x) d x

cos (5) - cos (4)

Decimal Notation

0.93730 \dots

Solution steps

\int_{5}^{4} sin (x) d x

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

= - \int_{4}^{5} sin (x) d x

Use the common integral:

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

= - [- cos (x)]_{4}^{5}

Compute the boundaries:

- cos (5) + cos (4)

= - (- cos (5) + cos (4))

Simplify

= cos (5) - cos (4)

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What is the integral from 5 to 4 of sin(x) ?
The integral from 5 to 4 of sin(x) is cos(5)-cos(4)