CBSE Class 12-science Answered

Evaluate :

Asked by ahuja8087 | 16 Mar, 2017, 05:14: PM

Expert Answer

$begin mathsize 16px style straight I equals integral open parentheses 2 sin 2 straight x minus cosx close parentheses square root of 6 minus cos squared straight x minus 4 sinx end root dx equals integral open parentheses 2 sinxcosx minus cosx close parentheses square root of 6 minus open parentheses 1 minus sin squared straight x close parentheses minus 4 sinx end root dx Let comma space sinx space equals space straight t cosx space dx space equals space dt straight I equals integral open parentheses 2 sinx minus 1 close parentheses square root of 6 minus open parentheses 1 minus sin squared straight x close parentheses minus 4 sinx end root space cosx space dx straight I equals integral open parentheses 2 straight t minus 1 close parentheses square root of 6 minus open parentheses 1 minus straight t squared close parentheses minus 4 straight t end root space dt straight I equals integral open parentheses 2 straight t minus 1 close parentheses square root of 6 minus 1 plus straight t squared minus 4 straight t end root space dt straight I equals integral open parentheses 2 straight t minus 1 close parentheses square root of 5 plus straight t squared minus 4 straight t end root space dt straight I equals integral open parentheses 2 straight t minus 4 plus 4 minus 1 close parentheses square root of 5 plus straight t squared minus 4 straight t end root space dt straight I equals integral open parentheses 2 straight t minus 4 plus 3 close parentheses square root of 5 plus straight t squared minus 4 straight t end root space dt straight I equals integral open parentheses 2 straight t minus 4 close parentheses square root of 5 plus straight t squared minus 4 straight t end root space dt plus integral 3 square root of 5 plus straight t squared minus 4 straight t end root space dt For space the space first space integral comma space 2 straight t minus 4 space this space is space derivative space of space 5 plus straight t squared minus 4 t. Also comma space second space integral space you space can space solve space using space completing space square space method. end style$