question_answer

The area bounded by the curve \[y=x,\]\[x-\] axis and ordinates \[x=-1\]to \[x=2\] is

A)  0                                            

B)         \[\frac{1}{2}\]                  

C)         \[\frac{3}{2}\]                                  

D)         \[\frac{5}{2}\]

Correct Answer: D

Solution :

Bounded area \[\left| \int_{-1}^{0}{x\,dx} \right|+\left| \int_{0}^{2}{x\,dx} \right|\] \[=\left| -\frac{1}{2} \right|+|2|=2+\frac{1}{2}=\frac{5}{2}\]