JEE Mains · Maths · STD 12 - 7.2 definite integral
Let \([t]\) denote the greatest integer less than or equal to \(t\). Then the value of the integral \(\int_{-3}^{101}\left([\sin (\pi x)]+e^{[\cos (2 \pi x)]}\right) d x\) is equal to
- A \(\frac{52(1- e )}{ e }\)
- B \(\frac{52}{ e }\)
- C \(\frac{52(2+e)}{e}\)
- D \(\frac{104}{e}\)
Answer & Solution
Correct Answer
(B) \(\frac{52}{ e }\)
Step-by-step Solution
Detailed explanation
\(I=\int_{-3}^{101}\left([\sin (\pi x)]+e^{[\cos (2 \pi x)]}\right) d x\) \([\sin \pi x]\) is periodic with period 2 and \(e^{[\cos (2 \pi x)]}\) is periodic with period \(1 .\) So, \(I=52 \int_{0}^{2}\left([\sin \pi x]+e^{[\cos 2 \pi x]}\right) d x\)…
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