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Q.

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

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a

32

b

34

c

3

d

38

answer is D.

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Detailed Solution

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 .