JEE Mains · Maths · STD 12 - 7.2 definite integral
Let \(f: R \rightarrow R\) be a function defined as \(f(x)=a \sin \left(\frac{\pi[x]}{2}\right)+[2-x], a \in R\), where [t] is the greatest integer less than or equal to \(t\). If \(\lim _{x \rightarrow-1} f(x)\) exists, then the value of \(\int_{0}^{4} f(x) d x\) is equal to.
- A \(-1\)
- B \(-2\)
- C \(1\)
- D \(2\)
Answer & Solution
Correct Answer
(B) \(-2\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow-1^{+}} a \sin \left(\pi \frac{[x]}{2}\right)+[2-x]=-a+2\) \(\lim _{x \rightarrow-1^{-}} \operatorname{asin}\left(\pi \frac{[x]}{2}\right)+[2-x]=0+3=3\) \(\lim _{x \rightarrow-1} f(x)\) exist when \(a=-1\) Now,…
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