【正确答案】F(2a)一2F(a)=∫₀^2af(t)f'(2a一t)dt一2∫₀^af(t)f'(2a一t)dt
=一∫_a^2af(t)df(2a一t)一∫₀^af(t)f'(2a一t)dt
=一f(t)f(2a一t)｜₀^2a+∫₀^2af'(t)f(2a一t)dx一∫₀^af(t)f'(2a一t)dt
=f²(a)一f(0)f(2a)+∫_a^2af'(t)f(2a—t)dx一∫₀^af(t)f'(2a一t)dt
=f²(a)一f(2a)f(0)+∫₀^af'(2a一u)f(u)du—∫₀^af(t)f'(2a—t)dt
=f²(a)一f(2a)f(0)。