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

Question

The integral ∫ π 4 3 π 4 d x 1 + cos x is equal to, - 2, 2, 4, - 1

MARKS App · Accepted Answer

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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