WBJEE · Maths · Definite Integration
If [a] denote the greatest integer which is less than or equal to a. Then, the value of the integral \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}[\sin x \cos x] d x\) is
- A \(\frac{\pi}{2}\)
- B \(\pi\)
- C \(-\pi\)
- D \(-\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(D) \(-\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
Let \(/=\int_{-\pi / 2}^{\pi / 2}[\sin x \cdot \cos x] d x=\int_{-\pi / 2}^{\pi / 2}\left[\frac{1}{2} \sin 2 x\right] d x\) Put \(\theta=2 x \Rightarrow d \theta=2 d x\) Also, when \(\quad x=-\pi / 2,\) then \(\theta=-\pi\) when \(\quad x=\frac{\pi}{2},\) then \(\theta=\pi\)…
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