What is dx equal to ?

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NDA 02/2022 Mathematics Official Paper (Held On 04 Sep 2022)
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  1.  + c
  2.  + c
  3.  + c
  4.  + c

Answer (Detailed Solution Below)

Option 3 :  + c
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NDA 01/2025: English Subject Test
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Detailed Solution

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Given,

I = 

⇒ I = 

⇒ I =  = I1 - I2 (let)

Computing I1,

I1 = 

Put sin x = t → cos x dx = dt

⇒ I1

⇒ I1 = 

⇒ I1 = 

Similarly, 

I2 = 

Put cos x = t → - sin x dx = dt

⇒ I2 =  

⇒ I2 =  

⇒ I2 =  

Putting these value in I,

⇒ I = I1 - I2 =  - 

⇒ I =  + c

∴ The correct answer is option (3).

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