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CBSE Class 12-science Answered

Integration ( 2 sin 2 thita – cos thita) dthita/(6 – cos2thita – 4 sin thita)
Asked by haroonrashidgkp | 03 Nov, 2018, 06:49: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight I equals integral fraction numerator 2 sin 2 straight theta minus cosθ over denominator 6 minus cos squared straight theta minus 4 sinθ end fraction dθ straight I equals integral fraction numerator 2 cross times 2 sinθcosθ minus cosθ over denominator 6 minus open parentheses 1 minus sin squared straight theta close parentheses minus 4 sinθ end fraction dθ straight I equals integral fraction numerator cosθ left parenthesis 4 sinθ minus 1 right parenthesis dθ over denominator 5 plus sin squared straight theta minus 4 sinθ end fraction Put space sinθ equals straight t cosθdθ equals dt straight I equals integral fraction numerator 4 straight t minus 1 over denominator 5 plus straight t squared minus 4 straight t end fraction dt Consider comma 4 straight t minus 1 equals straight A straight d over dt open parentheses 5 plus straight t squared minus 4 straight t close parentheses plus straight B 4 straight t minus 1 equals straight A left parenthesis 2 straight t minus 4 right parenthesis plus straight B 4 straight t minus 1 equals 2 At minus 4 straight A plus straight B 2 straight A equals 4 straight A equals 2 and space minus 4 straight A plus straight B equals negative 1 minus 8 plus straight B equals negative 1 straight B equals 7 straight I equals integral fraction numerator 2 left parenthesis 2 straight t minus 4 right parenthesis plus 7 over denominator 5 plus straight t squared minus 4 straight t end fraction dt straight I equals integral open parentheses fraction numerator 2 left parenthesis 2 straight t minus 4 right parenthesis over denominator 5 plus straight t squared minus 4 straight t end fraction plus fraction numerator 7 over denominator 5 plus straight t squared minus 4 straight t end fraction close parentheses dt Integrate space it space further. end style
Answered by Sneha shidid | 06 Nov, 2018, 11:18: AM

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