Integrate the functions: xx+4, x > 0 - Mathematics

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Sum

Integrate the functions:

`x/(sqrt(x+ 4))`, x > 0 

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Solution

Let I = `int x/ (sqrt( x + 4)) dx`

Put x + 4 = t

⇒ dx = dt . Also, x = t - 4

∴ `I = int (t - 4)/sqrtt dt`

`= int (t^(1/2) - 4t^ (-1/2)) dt`

`= 2/3 t^(3/2) -4 xx 2t^(1/2) + C`

`= 2/3 (x + 4)^(3/2) - 8 (x + 4)^(1/2) + C`

`= 2/3 (x + 4)^(1/2) [x + 4 - 12] + C`

`= 2/3 (x + 4)^(1/2) (x - 8) + C`

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Chapter 7: Integrals - Exercise 7.2 [Page 304]

APPEARS IN

NCERT Mathematics Class 12
Chapter 7 Integrals
Exercise 7.2 | Q 11 | Page 304
NCERT Mathematics Class 12
Chapter 7 Integrals
Exercise 7.2 | Q 11 | Page 304

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