JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

Let

f\left( x \right)

be an integrable function defined on

\left[ {a,\,\,b} \right],\,\,b\,\,\, > \,\,\,a\,\,\, > \,\,0

{I_1} = \int \limits_{\pi /6}^{\pi /3} \,\,f\,\,\left( {\tan \,\,\theta \,\, + \,\,\cot \,\,\theta } \right){\sec ^2}\,\,\theta \,\,d\theta

and,

{I_2} = \int \limits_{\pi /6}^{\pi /3} \,\,f\left( {\tan \,\,\theta \,\, + \,\,\cot \,\,\theta } \right)\,\,\mathrm{cose}{\mathrm{c}^2}\,\,\theta \,\,d\theta

, then

\frac{{{I_1}}}{{{I_2}}} =

View answer and explanation

Correct option: A

A positive integer

Option A (A positive integer) is correct because the integral I1 equals I2, making the ratio equal to 1, which is a positive integer.

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