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प्रश्न
Integrate the function:
`sqrt(4 - x^2)`
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उत्तर
Let `I = int sqrt (4 - x^2) dx`
`= int sqrt ((2)^2 - x^2) dx`
`= [x /2 sqrt ((2)^2 - x^2) + 4/2 sin^-1 (x/2)] + C` `...[int sqrt (a^2 - x^2) dx = x/2 sqrt (a^2 - x^2) + a^2/2 sin^-1 (x/a) + C]`
`= (x sqrt 4 - x^2)/2 + 4/2 sin^-1 (x/2) +C`
`(x sqrt(4 - x^2))/2 + 2 sin^-1 (x/2) + C`
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