JEE Mains · Maths · STD 12 - 7.2 definite integral
\(\int_{0}^{2}\left(\left|2 x^{2}-3 x\right|+\left[x-\frac{1}{2}\right]\right) d x\),where is the greatest integer function, is equal to.
- A \(\frac{7}{6}\)
- B \(\frac{19}{12}\)
- C \(\frac{31}{12}\)
- D \(\frac{3}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{19}{12}\)
Step-by-step Solution
Detailed explanation
\(\int_{0}^{2}\left|2 x ^{2}-3 x \right| dx\) \(=\int_{0}^{\frac{3}{2}}\left(3 x -2 x ^{2}\right) dx +\int_{\frac{3}{2}}^{2}\left(2 x ^{2}-3 x \right) dx =\frac{19}{12} .\) \(\int_{0}^{2}\left[ x -\frac{1}{2}\right] dx =\int_{\frac{-1}{2}}^{\frac{3}{2}}[ t ] dt\)…
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