What is the integral from 0 to 2 of (sin(pix))/(pix) ?

The integral from 0 to 2 of (sin(pix))/(pix) is 1/pi \Si(2pi)

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integral from 0 to 2 of (sin(pix))/(pix)

\int_{0}^{2} \frac{sin ( π x )}{π x} d x

\frac{1}{π} Si (2 π)

Solution steps

\int_{0}^{2} \frac{sin ( π x )}{π x} d x

Take the constant out:

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

= \frac{1}{π} \cdot \int_{0}^{2} \frac{sin ( π x )}{x} d x

Apply u-substitution

: \int_{0}^{π 2} \frac{sin ( u )}{u} d u

= \frac{1}{π} \cdot \int_{0}^{π 2} \frac{sin ( u )}{u} d u

Use the nonelementary integral:

\int \frac{sin ( x )}{x} d x = Si (x)

= \frac{1}{π} [Si (u)]_{0}^{π 2}

Compute the boundaries:

Si (2 π)

= \frac{1}{π} Si (2 π)

\int_{2}^{3} x (3 - x) d x

\int_{5}^{10} \frac{10 - x}{25} d x

\int_{0}^{2 π} - 98 sin^{2} (t) d t

\int_{0}^{x} 2 - t d t

\int_{- 2}^{1} x^{- 2} d x

What is the integral from 0 to 2 of (sin(pix))/(pix) ?
The integral from 0 to 2 of (sin(pix))/(pix) is 1/pi \Si(2pi)