integral space c o t space x space square root of cos e c space x space end root space d x

Asked by keshavvbhutraa | 20th Apr, 2020, 04:26: PM

Expert Answer:

To find integral of cot x sqrt{cosec x}
I equals integral c o t space x square root of cos e c space x end root space d x
equals integral fraction numerator cos space x over denominator sin space x end fraction cross times fraction numerator 1 over denominator square root of sin space x end root end fraction space d x
equals integral fraction numerator cos space x over denominator sin to the power of 3 divided by 2 end exponent x end fraction space d x
T a k e space sin space x equals u space rightwards double arrow space cos space x space d x equals d u
T h e r e f o r e comma space w e space h a v e
I equals integral 1 over u to the power of 3 divided by 2 end exponent d u
equals integral u to the power of negative 3 divided by 2 end exponent space d u
equals negative 2 over u to the power of 1 divided by 2 end exponent
equals negative fraction numerator 2 over denominator square root of sin space x end root end fraction

Answered by Renu Varma | 21st Apr, 2020, 12:00: AM