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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((1)^2−(2x)^2)dx`
Let `2x=t=>2dx=dt`
`∴I=1/2 int sqrt((1)^2−(t)^2)dt`
We know that, `int sqrt(a^2−x^2)dx=x/2 sqrt(a^2−x^2)+(a^2)/2 sin^(−1)(x/a)+C`
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