integral root of (a-x)/(a+x)
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Answered by
5
★★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
Answered by
0
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
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