Question

${\int }_a^{b}f(a+b-x)dx={\int }_a^{b}f\left(x\right)dx$ is true

• A. For all values of a,b
• B. For a $=$ 0 only
• C. For all values of a only
• D. For all values of b only

Answer 1

The correct option is A For all values of a,b

${\int }_a^{b}f(a+b-x)dx={\int }_a^{b}f\left(x\right)dx$
${\int }_a^{b}f(a+b-x)dx$
$a+b-x=t$
$-{\int }_b^{a}f\left(t\right)\cdot dt={\int }_a^{b}f\left(t\right)dt={\int }_a^{b}f\left(x\right)dx$
${\int }_a^{b}f(a+b-x)dx={\int }_a^{b}f\left(x\right)dx$ for all
value of a, b