Question #f09cc

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Answer 1 · 2017-10-05T23:26:33

$-cospix+c$

$int pisinpix$

We bring out the constant $pi$ outside the integral

$piintsinpix$

Now we can apply U-Substitution

$Let$ $u=pix$

$piintsinu$ $dx$

$(du)/dx=pi$

We want to get $du$ by itself so we multiply both sides by $dx$ .

$du=pi$ $dx$

$color(blue)piintsinu$ $color(blue)dx$

Since we have $color(blue)pi$ $color(blue)dx$ in the integral we can substitute it for $du$ .

$intsinu$ $du$

Now since everything is in terms of $du$ you can integrate:

$intsinu$ $du$ $rArr$ $-cosu+c$

Substitute $u$ into the answer:

$-cospix+c$