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AP EAMCET · Maths · Definite Integration

[ . ] represents greatest integer function, then \(\int_{-1}^1(x[1+\sin \pi x]+1) d x=\)

  1. A \(1\)
  2. B \(2\)
  3. C \(\frac{5}{2}\)
  4. D \(\frac{3}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{5}{2}\)

Step-by-step Solution

Detailed explanation

\(\int_{-1}^1(x[1+\sin \pi x]+1) d x\) \(I=\int_{-1}^1(x[1+\sin \pi x]+1) d x\) We know that, \(-1 \leq \sin \pi x \leq 1\) \(I=\int_{-1}^0(x[1+\sin \pi x]+1) d x+\int_0^1(x(1+\sin \pi x)+1) d x\)…