Question

Which formula is \[P_5\] : Halving the Upper Limit (Addition)?

Options

• \[\int_{0}^{2a} f(x)\,dx=\int_{0}^{a} f(x)\,dx+\int_{0}^{a} f(2a-x)\,dx\]

• \[\int_{0}^{2a} f(x)\,dx=0\]

• \[\int_{0}^{a} f(x)\,dx=\int_{0}^{a} f(a-x)\,dx\]

• \[\int_{0}^{2a} f(x)\,dx=2\int_{0}^{a} f(x)\,dx\]

Answer 1

\[P_5\] halves the upper limit \[2a\] into integrals with upper limit \[a\]. The second integrand is \[f(2a-x)\].