JEE Mains · Maths · STD 12 - 7.2 definite integral
If \([ t ]\) denotes the greatest integer \(\leq t\), then the value of \(\int_{0}^{1}\left[2 x-\left|3 x^{2}-5 x+2\right|+1\right] d x\) is.
- A \(\frac{\sqrt{37}+\sqrt{13}-4}{6}\)
- B \(\frac{\sqrt{37}-\sqrt{13}-4}{6}\)
- C \(\frac{-\sqrt{37}-\sqrt{13}+4}{6}\)
- D \(\frac{-\sqrt{37}+\sqrt{13}+4}{6}\)
Answer & Solution
Correct Answer
(A) \(\frac{\sqrt{37}+\sqrt{13}-4}{6}\)
Step-by-step Solution
Detailed explanation
\(I=\int \limits_{0}^{1}\left[2 x-\left|3 x^{2}-3 x-2 x+2\right|+1\right] d x\) \(I=\int \limits_{0}^{1}[2 x-|(3 x-2)(x-1)|] d x+\int_{0}^{1} 1 d x\)…
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