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Question Number 192687 by Mastermind last updated on 24/May/23

(1/π)∫_0 ^(2π) xcos(nx)dx Help!

1π∫02πxcos(nx)dxHelp!

Answered by Subhi last updated on 24/May/23

x=u ⇛ du = dx cos(nx)dx = dv v=(1/n)∫n.cos(nx) = (1/n).sin(nx) ∫u.dv = u.v−∫v.du = x.((sin(nx))/n)−(1/n)∫sin(nx).dx x.((sin(nx))/n)+(1/n^2 )∫−n.sin(nx).dx x.((sin(nx))/n)+(1/n^2 ).cos(nx)+c (1/π)∫x.cos(nx)dx = x.((sin(nx))/(nπ))+(1/(n^2 .π))cos(nx)+c

x=u⇛du=dxcos(nx)dx=dvv=1n∫n.cos(nx)=1n.sin(nx)∫u.dv=u.v−∫v.du=x.sin(nx)n−1n∫sin(nx).dxx.sin(nx)n+1n2∫−n.sin(nx).dxx.sin(nx)n+1n2.cos(nx)+c1π∫x.cos(nx)dx=x.sin(nx)nπ+1n2.πcos(nx)+c

Commented by Subhi last updated on 24/May/23

to find the definite integral, it will differ if (n) is integer or fraction

tofindthedefiniteintegral,itwilldifferif(n)isintegerorfraction

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