Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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Choose the correct alternative from the following. ∫dx(x - 8)(x + 7)= - Mathematics

MCQ

Choose the correct alternative from the following.

`int "dx"/(("x - 8")("x + 7"))`= 

Options

  • `1/15 log |("x" + 2)/("x - 1")|` + c

  • `1/15 log |("x + 8")/("x + 7")|` + c

  • `1/15 log |("x - 8")/("x + 7")|` + c

  • (x - 8)(x - 7) + c

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Solution

`1/15 log |("x - 8")/("x + 7")|` + c

Explanation:

Let I = `int "dx"/(("x - 8")("x + 7"))`

`= 1/15 int (15 * "dx")/(("x - 8")("x + 7"))`

`= 1/15 int (("x + 7") - ("x - 8"))/(("x - 8")("x + 7"))` dx

`= 1/15 (int 1/"x - 8" - int 1/"x + 7")` dx

`= 1/15 [log |"x - 8"| - log |"x + 7"|] + "c"`

`= 1/15 log |("x - 8")/("x + 7")|` + 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 1.06 | Page 137
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