JEE Mains · Maths · STD 12 - 7.2 definite integral
Let \(\displaystyle\int_{-2}^{2} (|\sin x| + [x \sin x])\,dx = 2(3 - \cos 2) + \beta\), where \([\cdot]\) is the greatest integer function. Then \(\beta \sin\left(\dfrac{\beta}{2}\right)\) equals:
- A \(1\)
- B \(2\)
- C \(4\)
- D \(8\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
Let \(I = \displaystyle\int_{-2}^{2} \left(|\sin x| + [x \sin x]\right) dx = I_1 + I_2\), where \(I_1 = \displaystyle\int_{-2}^{2} |\sin x|\, dx\) and \(I_2 = \displaystyle\int_{-2}^{2} [x \sin x]\, dx\). Evaluating \(I_1\): Since \(|\sin x|\) is even,…
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