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Yotta Paper 2 · Q8

Paper 2Logic & proofCalculusGeometry

Find a counterexample, if it exists, to the statement:

∫01f(x) dx\int_0^1 f(x)\,\dd x is equal to the area enclosed by f(x)f(x), the xx-axis, x=0x=0 and x=1x=1 if f(x)f(x) is defined for 0≤x≤10\le x\le1.

Af(x)=(x−2)2f(x)=(x-2)^2
Bf(x)=(sin⁡(x)+1)(sin⁡(x)−1)f(x)=(\sin(x)+1)(\sin(x)-1)
Cf(x)=ln⁡(x)f(x)=\ln(x)
Df(x)=1−xf(x)=1-x
Ef(x)=cos⁡(x)f(x)=\cos(x)
FThe statement is incorrect, but none of the above are counterexamples
GThe statement is correct, so none of the above are counterexamples

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