#### To determine

**To find:**

The area of the region bounded by the given curves.

#### Answer

83

#### 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=x2 and y=4x-x2.

**3) Calculation:**

As the given region is bounded by curves y=x2 and y=4x-x2,

From graph, the upper boundary curve is y=4x-x2, and the lower boundary curve is y=x2

When the curves y=x2 and y=4x-x2 intersect each other; we have, x2=4x-x2

2x2-4x=0

x=0 or x=2

Therefore, the area of the region bounded by the curves y=x2 and y=4x-x2 between x=0 to x=2 is given by

A= ∫024x-x2-x2dx

= ∫024x-2x2dx

By using fundamental theorem of calculus and power rule,

A=4x22-2x3302

=222-2233-202-2033

=8-163=24-163

A=83

**Conclusion:**

The area of the region bounded by the curves y=x2 and y=4x-x2 between x=0 to x=2 is A=83