Integrate the following functions with respect to x: 9-(2x+5)2

Integrate the following functions with respect to x:

`sqrt(9 - (2x + 5)^2`

बेरीज

`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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पाठ 11: Integral Calculus - Exercise 11.12 [पृष्ठ २२५]

पाठ 11 Integral Calculus
Exercise 11.12 | Q 2. (i) | पृष्ठ २२५

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