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Column I, Column II A tx=1,f(x)={logx...

Column I, Column II `A tx=1,f(x)={logx ,x<1 2x-x^2, xgeq1` , p. is increasing At `x=2,f(x)={x-1,x<2 0,x=2sinx ,x >2` , q. is decreasing At `x=0,f(x)={2x+3,x<0 5,x=0x^2+7,x >0` , r. has point of maxima At `x=0,f(x)={e^(-x)x<0 0,x=0-cosx ,x >0` , s. has point of minima

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Verified by Experts

`f(x)=min(|x|,1-|x|,1/4)`

Now, from the figure,
`int_(-1)^(1)f(x)dx=2` (Area of trapezium OABC)
`=2(1/2(1 + 1/2)1/4)=3/8`
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CENGAGE PUBLICATION-DEFINITE INTEGRATION -JEE ADVANCED
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