Evaluate the following integral:
$integral subscript 0 superscript 1 fraction numerator 1 over denominator square root of 1 minus straight x squared end root end fraction dx$

Solution

Let I = $integral subscript 0 superscript 1 fraction numerator 1 over denominator square root of 1 minus straight x squared end root end fraction dx space equals space left square bracket sin to the power of negative 1 end exponent straight x right square bracket subscript 0 superscript 1 space equals space sin to the power of negative 1 end exponent 1 space minus space sin to the power of negative 1 end exponent 0 space equals space straight pi over 2 minus 0 space equals space straight pi over 2$

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Integrals

Evaluate the following integral:
$integral subscript 0 superscript 1 fraction numerator 1 over denominator square root of 1 minus straight x squared end root end fraction dx$

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