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Qiuyun TMUA Simulation Test Paper 2 · Q19

Paper 2Calculus

f(x)f(x) is continuous and now given the proposition

Z:∫02f(x)dx=0 and f(1)=0Z:\int_0^2f(x)\dd x=0\text{ and }f(1)=0

which of the following options correctly describes the relationship between the given proposition and the original proposition?

M:∫01f(x)dx=−∫12f(x)dxM:\int_0^1f(x)\dd x=-\int_1^2f(x)\dd x
N:f(x)+f(2−x)=0N:f(x)+f(2-x)=0
P:∫01f(x)dx=0 and f has a period of 1.P:\int_0^1f(x)\dd x=0\text{ and }f\text{ has a period of }1.
AMM is necessary and sufficient for ZZ; NN is necessary and sufficient for ZZ; PP is necessary and sufficient for ZZ.
BMM is necessary and sufficient for ZZ; NN is only sufficient for ZZ; PP is only necessary for ZZ.
CMM is only necessary for ZZ; NN is necessary and sufficient for ZZ; PP is only necessary for ZZ.
DMM is only necessary for ZZ; NN is only sufficient for ZZ; PP is neither necessary nor sufficient for ZZ.
EMM is necessary and sufficient for ZZ; NN is only sufficient for ZZ; PP is neither necessary nor sufficient for ZZ.

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