Find the intergral of the following:-
Asked by uma.therighter
| 13th Jun, 2009,
08:52: AM
Expert Answer:
1/(1+cotx) =sinx/(sinx+cosx) =1/2 ( 1+ (sinx-cosx)(sinx+cosx) )
Now I= ∫1/2 ( 1+ (sinx-cosx)(sinx+cosx) )dx=x/2 +1/2 ∫ (sinx-cosx)(sinx+cosx) dx
Put sinx+cosx=t in the second term,
1/2 ∫ (sinx-cosx)(sinx+cosx) dx=1/2 ∫ -dt/t = -1/2lnt
Hence I=x/2-1/2ln(sinx+cosx) +c
Similarily second can be solved.
Answered by
| 13th Jun, 2009,
06:43: PM
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