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Question

If for all real triplets (a,b,c), f(x)=a+bx+cx2; then 10f(x)dx is equal to :

A
2(3f(1)+2f(12))
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B
13(f(0)+f(12))
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C
12(f(1)+3f(12))
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D
16(f(0)+f(1)+4f(12))
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Solution

The correct option is D 16(f(0)+f(1)+4f(12))
f(x)=a+bx+cx2
f(0)=a, f(1)=a+b+c
f(12)=c4+b2+a

10f(x)dx=10(a+bx+cx2)dx
=a+b2+c3
=16(6a+3b+2c)
=16(a+(a+b+c)+(4a+2b+c))
=16(f(0)+f(1)+4f(12))

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