#### To determine

**To graph:**

The region between the curves and use the calculator to compute the area correct to five decimal places.

#### Answer

Area = 0.25142

#### Explanation

**1) Concept:**

Graph the two curves and set up the integral for the area using the concept of the area between the two curves.

Area between two curves:

The area between the curves y=fxand y=g(x) and between x=a and x= b, where f a nd g are the continuous functions is

A= ∫ab|fx-gx| dx

**2) Given:**

The equation of the curves y=tan2x and y=x

**3) Calculations:**

Graph g(x)=tan2x and f(x)=x on a calculator

The curves intersect at x =0 and x=0.74936

So, the area is given by ∫00.74936(x-tan2x) dx

Evaluate the integral using a calculator.

**Conclusion:**

Area = 0.25142