JEE Mains · Maths · STD 12 - 7.2 definite integral
If \([\,\,]\) denotes the greatest integer function, then the integral \(\int\limits_0^\pi {[\cos \,\,x\,\,dx]} \) is equal
- A \(\frac {\pi }{2}\)
- B \(0\)
- C \(-1\)
- D \(-\frac {\pi }{2}\)
Answer & Solution
Correct Answer
(D) \(-\frac {\pi }{2}\)
Step-by-step Solution
Detailed explanation
\(I = \int\limits_0^\pi {\left[ {\cos x} \right]dx\,\,\,\,\,.....\left( 1 \right)} \) \(I = \int\limits_0^\pi {\left[ {\cos \left( {\pi - x} \right)} \right]dx} \) \( = \int\limits_0^\pi {\left[ { - \cos x} \right]dx} \,\,\,\,\,......\left( 2 \right)\) On adding \((1)\) and…
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