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$If f (x) = min (| x |, 1 - | x |, \frac{1}{4}) \forall x \in R then find the value of \int_{- 1}^{1} f (x) d x .$

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Correct option is D

f(x)=min|x|,1−|x|,14Now, from figure, we have∫−11 f(x)dx=2( Area of trapezium OABC)=2×12×(AB+OC)×AM=2121+1214=38

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If f(x)=min|x|,1−|x|,14∀x∈R then find the value of ∫−11 f(x)dx .

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$If f (x) = min (| x |, 1 - | x |, \frac{1}{4}) \forall x \in R then find the value of \int_{- 1}^{1} f (x) d x .$