What is f(x) = int 2sinx-xcosx dx if f((7pi)/6) = 0 ?

1 Answer
Jun 14, 2018

f(x)=-3cosx-xsinx-(3sqrt3)/2-(7pi)/12

Explanation:

Split up the integral into
f(x)=2intsinxdx-intxcosxdx
Using integration by parts, we get
f(x)=-2cosx-xsinx-cosx+C
f(x)=-3cosx-xsinx+C
Substituting x=(7pi)/6, we get
f((7pi)/6)=0=-3cos((7pi)/6)-(7pi)/6sin((7pi)/6)+C
Solving for C, we get
C=-(3sqrt3)/2-(7pi)/12
Therefore, f(x)=-3cosx-xsinx-(3sqrt3)/2-(7pi)/12.