#### To determine

**To find:**

The area of the region bounded by the given curves.

#### Answer

712

#### Explanation

**1) Concept:**

The area A of the region bounded by the curves y=fx& y=gx and the lines x=a, x=b, where f and g are continuous and fx≥g(x) for all x in a, b, is

A= ∫abfx-gxdx

**2) Given:**

The region bounded by curves y=1-2x2 and y=|x|.

**3) Calculation:**

As the given region is bounded by curves y=1-2x2 and y=|x|,

From the graph, the region is symmetric about y axis.Therefore, consider x≥0 double the given area.

If x≥0, then x=x, and the graphs intersect when x=1-2x2. That is when

2x2+x-1=0

2x-1x+1=0

Therefore, either x=12 or x=-1, but -1<0 so x=12

Hence, the limits of integration is from x=0 to x=12

The upper boundary curve is y=1-2x2 and the lower boundary curve is y=x

Therefore, the area of the region bounded by the curves y=1-2x2 and y=|x| is given by

A= 2∫0121-2x2-xdx

= 2∫0121-x-2x2dx

By using fundamental theorem of calculus and power rule,

A=2x-x22-23x3012

=212-1222-23123-0-022-2303

=212-18-112=2(12-3-2)24

A=712

**Conclusion:**

The area of region bounded by curves y=1-2x2 and y=|x| is A=712 sq.unit