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Definite Integration question

2022 · 27 Jul · Shift 2 · Q26

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PYQ Library
JEE Main
Mathematics
Definite Integration
2022 · 27 Jul · Shift 2 · Q26

Definite Integration question

2022 · 27 Jul · Shift 2 · Q26

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

Let

f(x)=2+|x|-|x-1|+|x+1|, x \in \mathbf{R}

. Consider

(\mathrm{S} 1): f^{\prime}\left(-\frac{3}{2}\right)+f^{\prime}\left(-\frac{1}{2}\right)+f^{\prime}\left(\frac{1}{2}\right)+f^{\prime}\left(\frac{3}{2}\right)=2(\mathrm{S} 2): \int\limits_{-2}^{2} f(x) \mathrm{d} x=12

Then,

A
both (S1) and (S2) are correct
B
both (S1) and (S2) are wrong
C
only (S1) is correct
D
only (S2) is correct

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