What is the integral of sin((npix)/5) ?

The integral of sin((npix)/5) is -5/(pin)cos((pinx)/5)+C

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integral of sin((npix)/5)

\int sin (\frac{nπ x}{5}) d x

- \frac{5}{πn} cos (\frac{πn x}{5}) + C

Solution steps

\int sin (\frac{nπ x}{5}) d x

Apply u-substitution

: \int \frac{5 sin ( u )}{πn} d u

= \int \frac{5 sin ( u )}{πn} d u

Take the constant out:

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

= \frac{5}{πn} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{5}{πn} (- cos (u))

Substitute back

u = \frac{n x π}{5}

= \frac{5}{πn} (- cos (\frac{n x π}{5}))

Simplify

= - \frac{5}{πn} cos (\frac{πn x}{5})

Add a constant to the solution

= - \frac{5}{πn} cos (\frac{πn x}{5}) + C

y^{^{'}} = \frac{1}{x} y

x \to 0 - lim (e^{\frac{1}{x}})

\int \frac{36 x ^{2} - 1}{x} d x

(3 x - 2)^{2} (3 - x^{2})^{2}

\int (16 - x^{2}) d x

What is the integral of sin((npix)/5) ?
The integral of sin((npix)/5) is -5/(pin)cos((pinx)/5)+C