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Daniel J Smith Custom TMUA Set A Paper 1 · Q6

Paper 1CalculusAlgebra

Let ff be a polynomial defined for all real xx, and define

J=∫−23(f(x)−f(∣x∣)) dxJ=\int_{-2}^3\big(f(x)-f(|x|)\big)\,dx

Which of the following expressions is equal to JJ for all such polynomials ff?

A−∫02f(t) dt\displaystyle-\int_0^2 f(t)\,dt
B∫02f(t) dt\displaystyle\int_0^2 f(t)\,dt
C∫−20f(t) dt−∫02f(t) dt\displaystyle\int_{-2}^0 f(t)\,dt-\int_0^2 f(t)\,dt
D00
Ef(0)f(0)
Ff(2)−f(0)f(2)-f(0)
G∫−20f(t) dt\displaystyle\int_{-2}^0 f(t)\,dt

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