The function is .

(a) Show that for .

Consider .

The integral represents the area between the function and the -axis.

.

From the graph:

.

.

, for .

(b)

Graph the function as .

From the graph: .

(c)

Consider .

.

From part (a): .

.

Consider .

.

From part(b): .

.

Therefore, .

(d)

Consider .

.

.

.

By the squeeze theorem, .

(e)

Consider .

For , .

For , .

For , .

.

(a) , for .

(b)

Graph the function as .

(c) .

(d) .

(e)

For , .

For , .

For , .