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Question

Let f(x)=10t|tx|dt,xϵ R
f(6) equals

A
2083
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B
13
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C
23
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D
Not defined
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Solution

The correct option is A 2083
10t|tx|dx
x<0f(x)10t(tx)dx=(t33t22x)10=13x2
x>0f(x)10t(xt)dt=(t2x2t23)10=x213
0x1=x0(xt)dt+x0t(xt)dt
(t2x2t33)x0+(t33xt22)1x
=(x22x33)+(13x2)(x33x32)
f(x)=x32x2+13
Minimum value is possible at x=12
f(6)=2083

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