Comprehension

Direction : Consider the following for the items that follow :

Let , where f(x) = sin x and g(x) = sin x + cos x + 1

What is I equal to?

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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Answer (Detailed Solution Below)

Option 3 :
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Detailed Solution

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Concept:

Property of Definite Integrals (Symmetry):

  • If is continuous on , then .
  • This property helps in evaluating integrals involving trigonometric identities when limits are symmetric.
  • Standard result used: .
  • Combining two symmetrical integrals can simplify expressions and eliminate complex terms.

 

Calculation:

Let

⇒ Using substitution

⇒ Adding both expressions, we get:

∴ The value of the integral is .

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