InterviewSolution
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InterviewSolution
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फलन `int(dx)/(5+4 cos x)` का x के सापेक्ष समाकलन कीजिए। |
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Answer» माना `I=int(dx)/(5+4cosx)=int(dx)/(5+4((1-tan^(2)x//2)/(1+tan^(2)x//2)))` `=int((1+tan^(2)x//2)dx)/(5(1+tan^(2)x//2)+4(1-tan^(2)x//2))` `=int(sec^(2)x//2dx)/(9+tan^(2)x//2)=(1)/(9)int(sec^(2)x//2 dx)/(1+((tanx//2)/(3))^(2))` माना `(tanx//2)/(3)= t therefore sec^(2)x//2 dx=6dt` `therefore I=(6)/(9)int(dt)/(1+t^(2))=(2)/(3)tan^(-1)((tanx//2)/(3))` |
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