What is the integral of $int sin (pi x) dx$ ?

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Answer 1 · 2016-02-11T01:04:57

$(-cos(pix))/pi+C$

Noting that $intsin(x)dx=-cos(x)+C$ ,

Let $u=pix$ , so $du=pidx$ .

From here, we have

$=intsin(u)(1/pi)pidx$

Bring the constant out of the expression and replace $pidx$ with $du$ :

$=1/piintsin(u)du=-(1/pi)cos(u)+C$

Substituting $u=pix$ back in, we get a final answer of

$(-cos(pix))/pi+C$

What is the integral of int sin (pi x) dxint sin (pi x) dx?