integration of dx/x^1/2(5-x)^1/2

Asked by Balbir | 5th Oct, 2017, 12:11: PM

Expert Answer:

begin mathsize 16px style integral fraction numerator dx over denominator square root of straight x open parentheses 5 minus straight x close parentheses end root end fraction
integral fraction numerator dx over denominator square root of 5 straight x space minus space straight x squared end root end fraction
Third space term space equals space open parentheses 5 over 2 close parentheses squared space equals space 25 over 4
integral fraction numerator dx over denominator square root of 25 over 4 begin display style minus end style begin display style fraction numerator begin display style 25 end style over denominator begin display style 4 end style end fraction end style begin display style plus end style begin display style 5 end style begin display style straight x end style begin display style minus end style begin display style straight x squared end style end root end fraction
integral fraction numerator dx over denominator square root of space open parentheses 5 over 2 close parentheses squared minus open parentheses straight x squared space minus space 5 straight x space plus space fraction numerator begin display style 25 end style over denominator begin display style 4 end style end fraction close parentheses end root end fraction
integral fraction numerator dx over denominator square root of space open parentheses 5 over 2 close parentheses squared minus open parentheses straight x minus 5 over 2 close parentheses squared end root end fraction
integral fraction numerator dx over denominator square root of open parentheses 5 over 2 close parentheses squared minus open parentheses begin display style fraction numerator 2 straight x minus 5 over denominator 2 end fraction end style close parentheses squared end root end fraction
sin to the power of negative 1 end exponent space open parentheses fraction numerator 2 straight x minus 5 over denominator 5 end fraction close parentheses plus straight c end style

Answered by Sneha shidid | 27th Dec, 2017, 05:30: PM