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Question

If x0f(t) dt=x2+1xt2f(t) dt, then f(12) is:

A
1825
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B
45
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C
2425
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D
625
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Solution

The correct option is C 2425
x0f(t) dt=x2+1xt2f(t) dt
Differentiating w.r.t x
f(x)0=2x+0x2f(x)
f(x)=2x1+x2
f(x)=(1+x2)22x2x(1+x2)2
f(x)=22x2(1+x2)2
Hence, f(12)=2425

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