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Integrate the functionssqrt(1-4x^2)...

Integrate the functions`sqrt(1-4x^2)`

Text Solution

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`" Let " I= int sqrt(1-4x^(2))dx = int sqrt(4((1)/(4)-x^(2)))dx`
`=2 int sqrt[[((1)/(2))^(2)-x^(2)]]dx`
`=2. [(x)/(2) sqrt((1)/(2)-x^(2))+(1)/(4) .sin^(-1) .(x)/(1//2) ]+C`
`rArr I=(x)/(2) sqrt(1-4x^(2)) +(1)/(4) sin^(-1) .(2x)+C`
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