Q. $\int_{- 100}^{100}{f(x)}dx$ is equal to
A) $\int_{- 100}^{100}{f(x^{2})}dx$
B) $\int_{- 100}^{100}{f( - x^{2})}dx$
C) $\int_{- 100}^{100}{f\left( \frac{1}{x} \right)}dx$
D) $\int_{- 100}^{100}{f( - x)}dx$
Explanation
(d)
Put $x = - t$
$\Rightarrow dx = - dt$
$\therefore\int_{- 100}^{100}{f(x)dx}$
$= - \int_{100}^{- 100}{f( - t)dt}$
$= \int_{- 100}^{100}{f( - t)dt}$
$= \int_{- 100}^{100}{f( - x)dx}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.