# How do you find the integral #int_0^1x*sqrt(1-x^2)dx# ?

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To find the integral ( \int_{0}^{1} x \sqrt{1 - x^2} , dx ), you can use the substitution method. Let ( u = 1 - x^2 ), then ( du = -2x , dx ). Solving for ( dx ), we get ( dx = -\frac{du}{2x} ). Substituting these into the integral and adjusting the limits accordingly, you can integrate with respect to ( u ).

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