JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of the integral \(\int\limits_{ - 2}^2 {\frac{{{{\sin }^2}\,x}}{{\left[ {\frac{x}{\pi }} \right] + \frac{1}{2}}}\,\,dx} \) (where \([x]\) denotes the greatest integer less than or equal to \(x\) ) is
- A \(0\)
- B \(sin\,4\)
- C \(4\)
- D \(4\,-\,sin\,4\)
Answer & Solution
Correct Answer
(A) \(0\)
Step-by-step Solution
Detailed explanation
\(\int\limits_0^2 {\left( {\frac{{{{\sin }^2}x}}{{\frac{1}{2} + \left[ {\frac{x}{\pi }} \right]}} + \frac{{{{\sin }^2}x}}{{\frac{1}{2} + \left[ { - \frac{x}{\pi }} \right]}}} \right)dx} \)…
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