$\int\limits_{-\frac{5}{2}}^{\frac{5}{2}}|x|dx$ is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\frac{25}{4}$
$\int_{-5/2}^{5/2}|x|\,dx$
$|x|$ is an even function
$=2\int_{0}^{5/2}x\,dx$
$=2\left[\frac{x^2}{2}\right]_{0}^{5/2}$
$=2\cdot\frac{25}{8}$
$=\frac{25}{4}$
The value of the integral is $\frac{25}{4}$.