(a)

Step 1 :

The graphs of the equations are $\"\"$ and $\"\"$ .

Sketch the region bounded graphs :

Graph the functions $\"\"$ and $\"\"$ .

Shade the region bounded by the curves between $\"\"$ and $\"\"$ .

$\"\"$

Note : Here the intersection points are found by using graphing utility.

Observe the graph for intersection points are $\"\"$ and $\"\"$ .

Solution:

Regions bounded by the graphs of equations is

$\"\"$

(b)

Step 1 :

The equations are $\"\"$ and $\"\"$ .

Definite integral as area of the region:

If $\"image\"$ and $\"image\"$ are continuous and non-negative on the closed interval $\"image\"$ ,

then the area of the region bounded by the graphs of $\"image\"$ and $\"image\"$ and the vertical lines $\"image\"$ and $\"image\"$ is given by

$\"\"$ . \ \

So the area of region $\"\"$ .

Point of intersection :

The equations are $\"\"$ and $\"\"$ .

The intersections points can be found by equating the above two equations.

$\"\"$ \ \ It is difficult to find the intersection for cosine function and a curve equation.

Therefore, it is difficult to evaluate the Integral with out using graphing utility.

Solution:

Area of the region is difficult to find by hand. $\"\"$