Q37 / 116 · NTA Abhyas (JEE Main) 2020 · Mathematics · Definite Integration

Consider $A = \int_{0}^{\frac{π}{4}} \frac{s i n (2 x)}{x} d x,$ then

A
$A > \frac{π}{2}$
B
$A = \frac{π}{2}$
Correct answer
C
$A < \frac{π}{2}$
D
$A > π$

Solution

As

s i n θ < θ, \forall θ \in (0, \frac{π}{2})

∴ s i n (2 x) < 2 x

So,

A = 2 \int_{0}^{\frac{π}{4}} \frac{s i n (2 x)}{2 x} d x < 2 \int_{0}^{\frac{π}{4}} 1 d x

\Rightarrow A < 2 (\frac{π}{4}) = \frac{π}{2}

Hence, the correct answer is option: 'C'.

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