MHT CET · Maths · Definite Integration
\(\int_{-2}^{1}[x+1] d x=\)
(Where \([x]\) is greatest integer function not greater than \(x\) )
- A \(1\)
- B \(0\)
- C \(-1\)
- D \(2\)
Answer & Solution
Correct Answer
(B) \(0\)
Step-by-step Solution
Detailed explanation
\(\int_{-2}^{1}[x+1] d x =\int_{-2}^{-1}([x]+1) d x+\int_{-1}^{0}([x]+1) d y~+\) \(\int_{0}^{1}([x]+1) d x \)
\( =\int_{-2}^{-1}(-2+1) d x+\int_{-1}^{0}(-1+1) d x+\int_{0}^{1}(0+1) d x \)
\( =-[x]_{-2}^{-1}+0+[x]_{0}^{1}=-(-1+2)+0+(1-0) \)
\( =0\)
\( =\int_{-2}^{-1}(-2+1) d x+\int_{-1}^{0}(-1+1) d x+\int_{0}^{1}(0+1) d x \)
\( =-[x]_{-2}^{-1}+0+[x]_{0}^{1}=-(-1+2)+0+(1-0) \)
\( =0\)
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