Definite Integration Question 33

Question: $ \int _{-1}^{2}{|x|dx} $

[DCE 1999]

Options:

A) 5/2

B) 1/2

C) 3/2

D) 7/2

Show Answer

Answer:

Correct Answer: A

Solution:

$ I=\int _{-1}^{2}{|x|dx} $

$ =\int _{-1}^{0}{-xdx}+\int_0^{2}{xdx} $

$ =-[ \frac{x^{2}}{2} ] _{-1}^{0}+[ \frac{x^{2}}{2} ]_0^{2} $

$ =-[ 0-\frac{1}{2} ]+[2] $

$ =2+\frac{1}{2}=\frac{5}{2} $ .