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JEE Main2017MathematicsDefinite IntegrationActual

The integral ∫ π 4 3 π 4 d x 1 + cos x is equal to

Options

  1. A- 2
  2. B2
  3. C4
  4. D- 1

Correct answer

B. 2

Step-by-step solution

Let, I = ∫ π 4 3 π 4 d x 1 + cos x ⇒ I = ∫ π 4 3 π 4 d x 1 + 2 cos 2 x 2 - 1 ⇒ I = 1 2 ∫ π 4 3 π 4 sec 2 x 2   d x ⇒ I = tan x 2 π 4 3 π 4 ⇒ I = tan 3 π 8 - tan π 8 ⇒ I = 2 + 1 - 2 - 1 ⇒ I = 2 .

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