The value of the integral, $integral subscript 3 superscript 6 fraction numerator square root of straight x over denominator square root of 9 minus straight x end root plus square root of straight x end fraction dx$ is

1/2

3/2

2

1

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Solution

3/2

straight I space equals space integral subscript 3 superscript 6 fraction numerator square root of straight x over denominator square root of 9 minus straight x end root plus square root of straight x end fraction dx straight I space equals space integral subscript 3 superscript 6 fraction numerator square root of 9 minus straight x end root over denominator square root of 9 minus straight x end root plus square root of straight x end fraction dx 2 straight I space equals space integral subscript 3 superscript 6 dx space equals space 3 rightwards double arrow straight I space equals space 3 over 2

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