What is the integral from 0 to 10 of sin((pix)/(10)) ?

The integral from 0 to 10 of sin((pix)/(10)) is (20)/pi

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integral from 0 to 10 of sin((pix)/(10))

\int_{0}^{10} sin (\frac{π x}{10}) d x

\frac{20}{π}

Decimal

6.36619 \dots

Solution steps

\int_{0}^{10} sin (\frac{π x}{10}) d x

Apply u-substitution

= \int_{0}^{π} sin (u) \frac{10}{π} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{10}{π} \cdot \int_{0}^{π} sin (u) d u

Use the common integral:

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

= \frac{10}{π} [- cos (u)]_{0}^{π}

Compute the boundaries:

2

= \frac{10}{π} \cdot 2

Simplify

= \frac{20}{π}

What is the integral from 0 to 10 of sin((pix)/(10)) ?
The integral from 0 to 10 of sin((pix)/(10)) is (20)/pi