HSC Commerce (Marketing and Salesmanship) 12th Board ExamMaharashtra State Board
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Evaluate : ∫ Sin X √ Cos 2 X − 2 Cos X − 3 D X - HSC Commerce (Marketing and Salesmanship) 12th Board Exam - Mathematics and Statistics

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Question

Evaluate :`int Sinx/(sqrtCos^2 x-2 cos x-3)  dx`

Solution

`int Sinx/(sqrtCos^2 x-2 cos x-3)  dx`                          Put cos x = t
– sin x dx = dt
sin x dx = – dt 

 =`-int dt/(sqrt t^2-2t-3)` 

=`int dt /(sqrt ((t-1))^2-4)` 

                    (Completing the square) 

=`-int    dt/(sqrt(t-1)^2-(2)^2` 

                                              Put t – 1 = θ
dt = dθ 

=`-int (dθ)/(sqrt(θ^2-(2)^2)` 

=`-log|θ+sqrtθ-(-2)^2|+C` 

=`-Log|t-1+sqrt((t-1))^2-4|+C` 

=`-log|t-1+sqrt(t^2-2t-3)|+C` 

= `– log|cosx-1+sqrt(cos^2x-2cosx-3)|+C`

 

  Is there an error in this question or solution?

APPEARS IN

 2017-2018 (March) (with solutions)
Question 3.2.1 | 4.00 marks
Solution Evaluate : ∫ Sin X √ Cos 2 X − 2 Cos X − 3 D X Concept: Continuous Function of Point.
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