Choose the correct options from the given alternatives : ∫dxcosxsin2x-cos2x⋅dx = - Mathematics and Statistics

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MCQ

Choose the correct options from the given alternatives : 

`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =

Options

  • `log(tanx - sqrt(tan^2x - 1)) + c`

  • sin–1 (tan x) + c

  • 1 + sin–1 (cot x) + c

  • `log(tanx + sqrt(tan^2x - 1)) + c`

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Solution

`log(tanx + sqrt(tan^2x - 1)) + c`

[ Hint : `int dx/(cosxsqrt(sin^2x - cos^2x)`

= `int (sec2x*dx)/sqrt(tan2x - 1)`     ...[Dividing by cos2x]
Put tan x = t].

  Is there an error in this question or solution?
Chapter 3: Indefinite Integration - Miscellaneous Exercise 3 [Page 149]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 3 Indefinite Integration
Miscellaneous Exercise 3 | Q 1.16 | Page 149

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