Question

Which expression equals \[\int_{a}^{b} f(x)\,dx\] by \[P_3\] : The "King's Rule"?

Options

• \[\int_{a}^{b} f(a-b+x)\,dx\]

• \[\int_{a}^{b} f(a+b-x)\,dx\]

• \[\int_{0}^{a} f(a-x)\,dx\]

• \[\int_{-a}^{a} f(-x)\,dx\]

Answer 1

The "King's Rule" replaces \[x\] by \[a+b-x\]. It expresses symmetry on \[a,b\].