What is the integral of sin(pit) ?

The integral of sin(pit) is -1/pi cos(pit)+C

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integral of sin(pit)

\int sin (π t) d t

- \frac{1}{π} cos (π t) + C

Solution steps

\int sin (π t) d t

Apply u-substitution

: \int sin (u) \frac{1}{π} d u

= \int sin (u) \frac{1}{π} d u

Take the constant out:

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

= \frac{1}{π} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{π} (- cos (u))

Substitute back

u = π t

= \frac{1}{π} (- cos (π t))

Simplify

= - \frac{1}{π} cos (π t)

Add a constant to the solution

= - \frac{1}{π} cos (π t) + C

x \to \infty lim (\frac{x}{e})

\int cos^{3} (\frac{x}{20}) d x

y^{^{''}} - 4 y^{^{'}} = 0

\frac{x e ^{t}}{1 + x e ^{t}}

h \to \infty lim (\frac{2}{h} + 3)