$\"\"$

\

(a)

\

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

\

Graph the curves $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

\

Shade the region between the curves.

\

$\"\"$

\

Observe the graph:

\

Note : The region indicated in blue color is the region bounded by the four curves.

\

$\"\"$

\

(b)

\

Area of the region:

\

If $\"\"$ and $\"\"$ are continuous on $\"\"$ $\"\"$ for all $\"\"$ in $\"\"$ , and non-negative on the closed interval $\"\"$ , then the area of the region bounded by the graphs of $\"\"$ and $\"\"$ , and the vertical lines $\"\"$ and $\"\"$ is $\"\"$ .

\

Here $\"\"$ and $\"\"$ .

\

Observe the graph :

\

The region is bounded between $\"\"$ to $\"\"$ .

\

Area of the region is $\"\"$

\

$\"\"$ .

\

The intersections are difficult to find.

\

$\"\"$

\

(c)

\

Estimate the area by using graph:

\

$\"\"$

\

Observe the graph:

\

The area of the region is $\"\"$ sq-units.

\

$\"\"$

\

(a)

\

Graph the curves $\"\"$ , $\"\"$ and $\"\"$ .

\

$\"\"$

\

(b) $\"\"$ .

\

It is difficult to evaluate the integral since it does not have any elementary antiderivative.

\

(c)

\

The area of the region is $\"\"$ sq-units.