ISI2014-DCG-47

Question

The value of the definite integral $\int_0^{\pi} \mid \frac{1}{2} + \cos x \mid dx$ is

• A. $\frac{\pi}{6} + \sqrt{3}$
• B. $\frac{\pi}{6} - \sqrt{3}$
• C. $0$
• D. $\frac{1}{2}$

Comments

$0$ ??

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A  is the answer.

Answer 1

Answer is A.

| ½ + cosx | will be positive(>=0) in the interval [0,2pi/3],

while negative(<0) in the interval [2pi/3,pi].

Rest integrating the terms is straight forward.