Question

Which formula expresses \[P_1\] : Reversing Limits?

Options

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

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

• \[\int_{a}^{b} f(x)\,dx=\int_{a}^{c} f(x)\,dx+\int_{c}^{b} f(x)\,dx\]

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

Answer 1

Reversing Limits swaps the upper and lower limits. This changes the sign of the definite integral.