Archive
16th of March 2017
Mathematics
Q:

Evaluate :integral space left parenthesis space 2 sin 2 x space minus space cos x right parenthesis space square root of 6 minus cos squared space x minus 4 sin x end root space space space d x

Ahuja8087 Ahuja - CBSE - Class XII Science

Thursday, March 16, 2017 at 17:14:PM

A:

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

Thursday, March 16, 2017 at 17:55:PM