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Question

If f(x)=limn[2x+4x3+6x5+.......+2bx2n1] (0<x<1) then f(x) dx is equal to

A
1x2+c
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B
11x2+c
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C
1x21+c
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D
11x2+c
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Solution

The correct option is D 11x2+c
f(x)=limx[2x+4x3+6x5+........2+x(2x1)]=n=12nx2n10<x<1then,fxdx=n=12nx2n2n+C1=(1+n=1x2n+c)=n=0x2n+c=n=0(x2)n+c=1(1x2)+c

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