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- Jun 13, 2012
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S√sinx.dx
Hapa hakuna ujanja zaidi ya kutumia By-Part method.
ie. SVdU=UV-SUdV----eqn(a)
let dU=dx
Integrating both side
=>U=x------eqn(i)
and V=(sinx)^½
differentiating both sides
=>dV=(cosx)/(2√sinx)-------eqn(ii)
Substituting ---eqn(i)&(ii) into --eqn(a)
SVdU=x√sinx - 1/2S(xcosx)dx/(√sinx)
For S(xcosx)dx/(√sinx)
By By-Part tena
SUdV=UV-SVdU
Hapa let
U=x
=>dU=dx
And
dV=(cosx)/(√sinx)
Integrating both sides
=>V=2√sinx (kama hujaelewa hapo basi wewe ni kilaza)
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