JEE Mains · Maths · STD 12 - 7.2 definite integral
\(\int\limits_{0}^{5} \cos \left(\pi\left(x-\left[\frac{x}{2}\right]\right)\right) d x\) Where \([t]\) denotes greatest integer less than or equal to \(t\), is equal to
- A \(-3\)
- B \(-2\)
- C \(2\)
- D \(0\)
Answer & Solution
Correct Answer
(D) \(0\)
Step-by-step Solution
Detailed explanation
\(I=\int\limits_{0}^{5} \cos \left(\pi x-\pi\left[\frac{x}{2}\right]\right) d x\) \(\Rightarrow I=\int\limits_{0}^{2} \cos (\pi x) d x+\int\limits_{2}^{4} \cos (\pi x-\pi) d x+\int\limits_{4}^{5} \cos (\pi x-2 \pi) d x\)…
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