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Question
Integrate the following functions w.r.t. x : `sqrt((x - 3)(7 - x)`
Solution
Let I = `int sqrt((x - 3)(7 - x)).dx`
=`intsqrt(-x^2 + 10x - 21).dx`
= `int sqrt(- (x^2 - 10x + 21)).dx`
= `int sqrt(4 -(x^2 - 10x + 25)).dx`
= `int sqrt(2^2 - (x - 5)^2`
= `((x - 5)/2) sqrt(2^2 - (x - 5)^2) + 2^2/(2) sin^-1 ((x - 5)/2) + c`
= `((x - 5)/2) sqrt((x - 3)(7 - x)) + 2sin^-1 ((x - 5)/2) + c`.
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