alleryUsing the King's property, $\int_0^a f(x)\,dx$ equals:
A$\int_0^a f(a-x)\,dx$
B$\int_0^a f(a+x)\,dx$
C$\int_0^a f(x-a)\,dx$
D$-\int_0^a f(x)\,dx$
Answer & Solution
Correct answer: A. $\int_0^a f(a-x)\,dx$
Special case of King's property with $b = a$, lower = 0: $\int_0^a f(x)\,dx = \int_0^a f(0+a-x)\,dx = \int_0^a f(a-x)\,dx$.
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