tmua.fyi Mock Paper 2 · Question 8

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tmua.fyi Mock Paper 2 · Q8

Paper 2Logic & proofCalculusGeometryFunctions & graphs

Consider the statement: ‘If a function $g$ is defined on $[0,1]$ , then $\int_0^1 g(x)\,\dd x$ equals the area enclosed between the graph of $g$ and the $x$ -axis over $[0,1]$ .’ Which of the following is a counterexample?

g(x)=x^2

g(x)=x-1

g(x)=\frac1x

g(x)=1

Ethere is no counterexample

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