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#