What is the integral from 1 to 2 of cos(npix) ?

The integral from 1 to 2 of cos(npix) is (sin(2pin))/(pin)

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integral from 1 to 2 of cos(npix)

\int_{1}^{2} cos (nπ x) d x

\frac{sin ( 2 πn )}{πn}

Solution steps

\int_{1}^{2} cos (nπ x) d x

Apply u-substitution

= \int_{πn}^{nπ 2} \frac{cos ( u )}{πn} d u

Take the constant out:

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

= \frac{1}{πn} \cdot \int_{πn}^{nπ 2} cos (u) d u

Use the common integral:

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

= \frac{1}{πn} [sin (u)]_{πn}^{nπ 2}

Compute the boundaries:

sin (2 πn)

= \frac{1}{πn} sin (2 πn)

Simplify

= \frac{sin ( 2 πn )}{πn}

What is the integral from 1 to 2 of cos(npix) ?
The integral from 1 to 2 of cos(npix) is (sin(2pin))/(pin)