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

The integral from-1 to 1 of cos(npix) is 0

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integral from-1 to 1 of cos(npix)

\int_{- 1}^{1} cos (nπ x) d x

0

Solution steps

\int_{- 1}^{1} cos (nπ x) d x

Apply u-substitution

: \int_{- πn}^{πn} \frac{cos ( u )}{πn} d u

= \int_{- πn}^{πn} \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}^{πn} cos (u) d u

Use the common integral:

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

= \frac{1}{πn} [sin (u)]_{- πn}^{πn}

Compute the boundaries:

0

= \frac{1}{πn} \cdot 0

Simplify

= 0

x^{2} + 2 x y - y^{2} + x = 51, (5, 7)

(4.3) (4.6)

\int e^{- x} + e^{- 3 x} d x

n = 0 \sum \infty \frac{n !}{n ^{n}}

\int (\frac{1}{x ^{9}} - x^{9} - \frac{1}{8}) d x

What is the integral from-1 to 1 of cos(npix) ?
The integral from-1 to 1 of cos(npix) is 0