Evaluate the following: ∫1(x-3)(x+2).dx - Mathematics and Statistics

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Sum

Evaluate the following:

`int (1)/sqrt((x - 3)(x + 2)).dx`

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Solution

Let I = `int 1/sqrt((x - 3)(x + 2)).dx`

= `int 1/sqrt(x^2 - x - 6).dx`

= `int 1/sqrt((x^2 - x + 1/4) - 1/4 - 6).dx`

= `int 1/sqrt((x - 1/2)^2 - (5/2)^2).dx`

= `log|(x - 1/2) + sqrt((x - 1/2)^2 - (5/2)^2)| + c`

= `log|(x - 1/2) + sqrt(x^2 - x - 6)| + c`.

  Is there an error in this question or solution?
Chapter 3: Indefinite Integration - Exercise 3.2 (B) [Page 123]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 3 Indefinite Integration
Exercise 3.2 (B) | Q 1.17 | Page 123

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