12. What is the area of the closed region bounded by y = x2 - |x| and the x-axis, between x = -1 and x = 1?

 

A. 1/12

B. 1/6

C. 1/3

D. 2/3

E. 5/6

 

 

 Solution: The answer is C

 

To start, graph the curve y = x2 - |x|:

 

Note:

1) The region in question is enclosed by y = x2 - |x| and the x-axis.

2) y is an even function

3) The curve y = 0 is greater than the curve y = x2 - |x| for the interval [-1,1].

 

Thus the area of the enclosed region is given by evaluating the following integral:

 

By observation 3

 

By observation 2