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CBSE Class 12-science Answered

Integration  x(3x – 2)1/2 dx explain in great detail
Asked by haroonrashidgkp | 03 Oct, 2018, 08:59: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight I equals integral straight x square root of 3 straight x minus 2 end root dx
3 straight x minus 2 equals straight t
rightwards double arrow 3 straight x equals straight t plus 2
rightwards double arrow straight x equals fraction numerator straight t plus 2 over denominator 3 end fraction
3 dx equals dt
straight I equals integral open parentheses fraction numerator straight t plus 2 over denominator 3 end fraction cross times square root of straight t close parentheses dt
straight I equals 1 third integral open parentheses straight t to the power of 3 over 2 end exponent plus 2 straight t to the power of 1 half end exponent close parentheses dt
straight I equals 1 third open parentheses fraction numerator straight t to the power of begin display style 5 over 2 end style end exponent over denominator begin display style 5 over 2 end style end fraction plus fraction numerator 2 straight t to the power of begin display style 3 over 2 end style end exponent over denominator begin display style 3 over 2 end style end fraction close parentheses plus straight c
straight I equals 2 over 3 open parentheses open parentheses 3 straight x minus 2 close parentheses to the power of begin display style 5 over 2 end style end exponent over 5 plus fraction numerator 2 open parentheses 3 straight x minus 2 close parentheses to the power of 3 over 2 end exponent over denominator 3 end fraction close parentheses plus straight c end style
Answered by Sneha shidid | 04 Oct, 2018, 03:53: PM
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