#### To determine

**To graph:**

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

#### Answer

Area = 1.70413

#### Explanation

1) **Concept:**

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

Area between two curves:

The area between the curves y=fx and y=gx is

∫ab fx-g(x) dx

**2) Given:**

The equation of the curves y=cosx and y=x+sin4x

**3) Calculation:**

Graph f(x)=cosx and g(x)=x+2sin4x on a calculator.

The curves intersect at x =-1.911917 , x=-1.223676 and x=0.607946

So, the area is given by

∫-1.9119170.607946|(x+2sin4x)-cosx| dx

=∫-1.911917-1.223676[(x+2sin4x)-cosx] dx+∫-1.2236760.607946[cosx-(x+2sin4x)] dx

Evaluate it using a calculator.

Then the area is 1.70413

**Conclusion:**

Area = 1.70413