JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of the definite integral,

\int\limits_{{\theta_1}}^{\theta_2} \frac{{d} \theta}{1+\tan \theta}=\frac{501 \pi}{{K}}

where

\theta_2=\frac{1003 \pi}{2008}

and

\theta_1=\frac{\pi}{2008}

. The value of

K

equals

View answer and explanation

Correct option: D

2008

Option D (2008) is correct because the integral is evaluated using the property

\int_a^b f(x) dx = \int_a^b f(a+b-x) dx

and then comparing with the given form.

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