What is the integral of sin((pix)/a) ?

The integral of sin((pix)/a) is -a/pi cos((pix)/a)+C

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integral of sin((pix)/a)

\int sin (\frac{π x}{a}) d x

- \frac{a}{π} cos (\frac{π x}{a}) + C

Solution steps

\int sin (\frac{π x}{a}) d x

Apply u-substitution

: \int \frac{a sin ( u )}{π} d u

= \int \frac{a sin ( u )}{π} d u

Take the constant out:

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

= \frac{a}{π} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{a}{π} (- cos (u))

Substitute back

u = \frac{π x}{a}

= \frac{a}{π} (- cos (\frac{π x}{a}))

Simplify

= - \frac{a}{π} cos (\frac{π x}{a})

Add a constant to the solution

= - \frac{a}{π} cos (\frac{π x}{a}) + C

\frac{d}{d x} (\frac{x ^{2} - 6 x - 1}{( x - 3 ) ^{2}})

y^{^{''}} + 8 y^{^{'}} + 25 y = 0, y (0) = - 3, y^{^{'}} (0) = 1

\int_{- 5}^{3} ∣ x ∣ + 1 d x

n = 2 \sum \infty \frac{3}{6 ^{n}}

x \to 0 lim (e^{x} cos (5 x))

What is the integral of sin((pix)/a) ?
The integral of sin((pix)/a) is -a/pi cos((pix)/a)+C