jee-main 2022 Q74

jee-main · India · session2_29jul_shift2 Indefinite & Definite Integrals Piecewise/Periodic Function Integration
If $[t]$ denotes the greatest integer $\leq t$, then the value of $\int_0^1 \left[2x - \left|3x^2 - 5x + 2\right| + 1\right] dx$ is
(1) $\frac{\sqrt{37} + \sqrt{13} - 4}{6}$
(2) $\frac{\sqrt{37} - \sqrt{13} - 4}{6}$
(3) $\frac{-\sqrt{37} - \sqrt{13} + 4}{6}$
(4) $\frac{-\sqrt{37} + \sqrt{13} + 4}{6}$ 
If $[t]$ denotes the greatest integer $\leq t$, then the value of $\int_0^1 \left[2x - \left|3x^2 - 5x + 2\right| + 1\right] dx$ is\\
(1) $\frac{\sqrt{37} + \sqrt{13} - 4}{6}$\\
(2) $\frac{\sqrt{37} - \sqrt{13} - 4}{6}$\\
(3) $\frac{-\sqrt{37} - \sqrt{13} + 4}{6}$\\
(4) $\frac{-\sqrt{37} + \sqrt{13} + 4}{6}$
Paper Questions
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