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 \(\int \limits_{1}^{2}|2 x-[3 x]| d x\) is
- A \(1\)
- B \(2\)
- C \(4\)
- D \(3\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
\(3<3 x<6\) Take cases when \(3<3 x<4,4<3 x<5,\) \(5<3 x<6\) \(Now \int_{1}^{2}|2 x -[3 x ]| dx\) \(=\int_{1}^{4 / 3}(3-2 x) d x+\int_{4 / 3}^{5 / 3}(4-2 x) d x+\int_{5 / 3}^{2}(5-2 x) d x\) \(=\frac{2}{9}+\frac{3}{9}+\frac{4}{9}=1\)
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