Find begin mathsize 20px style integral sin to the power of negative 1 end exponent square root of fraction numerator x over denominator a plus x end fraction end root d x end style

Asked by sunil2791 | 4th Jul, 2017, 06:35: AM

Expert Answer:

begin mathsize 16px style straight I equals integral sin to the power of negative 1 end exponent square root of fraction numerator straight x over denominator straight a plus straight x end fraction end root dx
straight x equals atan squared straight t
rightwards double arrow dx equals straight a open parentheses 2 tantsec squared straight t close parentheses dt
straight I equals integral sin to the power of negative 1 end exponent square root of fraction numerator straight a tan squared straight t over denominator straight a plus straight a tan squared straight t end fraction end root straight a open parentheses 2 tantsec squared straight t close parentheses dt
straight I equals integral sin to the power of negative 1 end exponent square root of fraction numerator tan squared straight t over denominator 1 plus tan squared straight t end fraction end root straight a open parentheses 2 tantsec squared straight t close parentheses dt
straight I equals integral sin to the power of negative 1 end exponent square root of fraction numerator tan squared straight t over denominator sec squared straight t end fraction end root straight a open parentheses 2 tantsec squared straight t close parentheses dt
straight I equals 2 straight a integral sin to the power of negative 1 end exponent open parentheses sint close parentheses tant open parentheses 1 plus tan squared straight t close parentheses dt
straight I equals 2 straight a integral straight t space tant open parentheses 1 plus tan squared straight t close parentheses dt
straight I equals 2 straight a integral open parentheses straight t space tant plus straight t space tan cubed straight t close parentheses dt
Use space integration space by space parts space to space solve space both space the space terms.
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Answered by Sneha shidid | 4th Jul, 2017, 10:02: AM