Maharashtra State BoardHSC Commerce 12th Board Exam
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Evaluate ∫x - 1x + 4 dx - Mathematics and Statistics

Sum

Evaluate `int "x - 1"/sqrt("x + 4")` dx

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Solution

Let I = `int "x - 1"/sqrt("x + 4")` dx

= `int (("x + 4") - 5)/sqrt("x + 4")` dx

= `int (sqrt"x + 4" - 5/(sqrt "x + 4"))` dx

`= int [("x + 4")^(1/2) - 5("x + 4")^(- 1/2)]` dx

`= ("x + 4")^(3/2)/(3/2) - 5 ("x + 4")^(1/2)/(1/2)` + c

∴ I = `2/3 ("x + 4")^(3/2) - 10 sqrt("x + 4")` + c

  Is there an error in this question or solution?
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 5 Integration
Miscellaneous Exercise 5 | Q 4.1 | Page 138
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