What is the integral from 1 to 2 of sin(pix) ?

The integral from 1 to 2 of sin(pix) is -2/pi

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integral from 1 to 2 of sin(pix)

\int_{1}^{2} sin (π x) d x

- \frac{2}{π}

Decimal

- 0.63661 \dots

Solution steps

\int_{1}^{2} sin (π x) d x

Apply u-substitution

= \int_{π}^{π 2} sin (u) \frac{1}{π} d u

Take the constant out:

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

= \frac{1}{π} \cdot \int_{π}^{π 2} sin (u) d u

Use the common integral:

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

= \frac{1}{π} [- cos (u)]_{π}^{π 2}

Compute the boundaries:

- 2

= \frac{1}{π} (- 2)

Simplify

= - \frac{2}{π}

What is the integral from 1 to 2 of sin(pix) ?
The integral from 1 to 2 of sin(pix) is -2/pi