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JEE Main · 2017 · 02 Apr 2017 · Offline · Definite Integrals

The integral

\int_{\frac{π}{4}}^{\frac{3 π}{4}} \frac{d x}{1 + c o s x}

is equal to :

(A)-1
(B)-2
(C)2✓ Correct
(D)4

Answer: (C)

Solution

Use

1 + cos x = 2 cos^{2} \frac{x}{2}

, so

\int \frac{d x}{1 + cos x} = \int \frac{d x}{2 cos ^{2} ( x /2 )} = tan \frac{x}{2}

. Between

\frac{π}{4}

and

\frac{3 π}{4}

this is

tan \frac{3 π}{8} - tan \frac{π}{8} = (2 + 1) - (2 - 1) = 2

.

JEE Main · 2017 · 02 Apr 2017 · Offline · Single correct option

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