Question

integral root of (a-x)/(a+x)

Answer 1

★★Heya★★

Put x = a Cos ß

DIFFERENTIATE BOTH SIDES W.R.T x

dx = -a Sin ß dß

=>

integration of √{(a - x ) / ( a + x ) }dx is =

integration of ( Tan ß/2 ) × ( -a Sin ß ) dß

=>

integration of -a Sin² ß/2 dß

=>

integration of -a ( 1 - Cos ß )/2

=>

= -a ( ß - Sin ß )/2 + c

=>

= -a ( Cos-¹ ( x/a ) - Sin ( Cos-¹ ( x/a ) ) + c

Answer 2

Answer:

Step-by-step explanation:

Put x = a Cos ß

DIFFERENTIATE BOTH SIDES W.R.T x

dx = -a Sin ß dß

=>

integration of √{(a - x ) / ( a + x ) }dx is =

integration of ( Tan ß/2 ) × ( -a Sin ß ) dß

=>

integration of -a Sin² ß/2 dß

=>

integration of -a ( 1 - Cos ß )/2

=>

= -a ( ß - Sin ß )/2 + c

=>

= -a ( Cos-¹ ( x/a ) - Sin ( Cos-¹ ( x/a ) ) + c