JEE Main 202227 Jul, Evening shiftMathematicsMediumIntegral Calculus369× since 2002Let f(x)=2+∣x∣−∣x−1∣+∣x+1∣,x∈Rf(x)=2+|x|-|x-1|+|x+1|, x \in \mathbf{R}f(x)=2+∣x∣−∣x−1∣+∣x+1∣,x∈R. Consider (S1):f′(−32)+f′(−12)+f′(12)+f′(32)=2(\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(S1):f′(−23)+f′(−21)+f′(21)+f′(23)=2 (S2):∫−22f(x)dx=12(\mathrm{S} 2): \int\limits_{-2}^{2} f(x) \mathrm{d} x=12(S2):−2∫2f(x)dx=12 Then,AOption A. both (S1) and (S2) are correctBOption B. both (S1) and (S2) are wrongCOption C. only (S1) is correctDOption D. only (S2) is correctCheckSkip · show solution
