Find begin mathsize 20px style integral fraction numerator d x over denominator square root of open parentheses 1 plus sin x close parentheses end root end fraction end style (please give the answer before 8pm)

Asked by sunil2791 | 4th Jul, 2017, 05:51: PM

Expert Answer:

begin mathsize 16px style straight I equals integral fraction numerator dx over denominator square root of 1 plus sinx end root end fraction
straight I equals integral fraction numerator dx over denominator square root of 1 plus cos open parentheses begin display style straight pi over 2 end style minus straight x close parentheses end root end fraction
straight I equals integral fraction numerator dx over denominator square root of 2 cos squared open parentheses begin display style fraction numerator straight pi over 2 minus straight x over denominator 2 end fraction end style close parentheses end root end fraction
straight I equals integral fraction numerator 1 over denominator square root of 2 end fraction cross times fraction numerator dx over denominator cos open parentheses straight pi over 4 minus begin display style straight x over 2 end style close parentheses end fraction
straight I equals fraction numerator 1 over denominator square root of 2 end fraction integral sec open parentheses straight pi over 4 minus straight x over 2 close parentheses dx
straight I equals fraction numerator 1 over denominator square root of 2 end fraction log open vertical bar sec open parentheses straight pi over 4 minus straight x over 2 close parentheses plus tan open parentheses straight pi over 4 minus straight x over 2 close parentheses close vertical bar plus straight c
end style

Answered by Sneha shidid | 5th Jul, 2017, 09:09: AM