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If f(x)f(x)f(x) is a polynomial function that passes through origin, and g(x)=f′(x)g(x) = f'(x)g(x)=f′(x), then
g′(a)=f(a)g'(a) = f(a)g′(a)=f(a)
g′(a)=f′(a)g'(a) = f'(a)g′(a)=f′(a)
∫0ag(x)dx=f(a)\int_{0}^{a} g(x) dx = f(a)∫0ag(x)dx=f(a)
∫0af(x)dx=g(a)\int_{0}^{a} f(x) dx = g(a)∫0af(x)dx=g(a)
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