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Question

If f(x) is a continuous function such that f(x)0,x[2,10] and 84f(x)dx=0, then the value of f(6), is

A
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B
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C
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D
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Solution

The correct option is B 0
f(x) is above the x-axis or on the x-axis for all x[2,10].
If f(x) is greater than zero at any sub-interval of [4,8], then 84f(x)dx must be greater than zero.
But 84f(x)dx=0, which shows f(x) can't have any value greater than zero in the sub-interval [4,8].
f(x) is constant in the sub-interval [4,8] and has to be zero at all points, x[4,8].
f(x)=0,x[4,8]f(6)=0.
Ans: B

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