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Question
Integrate the following functions with respect to x:
`sqrt(9 - (2x + 5)^2`
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Solution
`int sqrt(9 - (2x + 5)^2) "d"x = int sqrt(3^2 - (2x + 5)^2) "d"x`
Put 2x + 5 = t
2 dx = dt
dx = `1/2 "dt"`
= `int sqrt(3^2 - "t"^2) xx 1/2 "dt"`
= `1/2 int sqrt(3^2 - "t"^2) "dt"`
= `1/2 ["t"/2 sqrt(3^2 - "t"^2) + 3^2/2 sin^-1 ("t"/3) + "c"]`
= `1/4 [(2x + 5) sqrt(9 - (2x + 5)^2) + 9 sin^-1 ((2x + 5)/3)] + "c"`
`int sqrt(9 - (2x + 5)^2) "d"x = 1/4 [(2x + 5) sqrt(9 - (2x + 5)^2) + 9 sin^-1 ((2x + 5)/3)] + "c"`
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