AP EAMCET · Maths · Definite Integration
[ . ] represents greatest integer function, then \(\int_{-1}^1(x[1+\sin \pi x]+1) d x=\)
- A \(1\)
- B \(2\)
- C \(\frac{5}{2}\)
- D \(\frac{3}{2}\)
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, \(-1 \leq \sin \pi x \leq 1\) \(I=\int_{-1}^0(x[1+\sin \pi x]+1) d x+\int_0^1(x(1+\sin \pi x)+1) d x\)…
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