Question

Determine a region whose area is equal to the given limit. Do not evaluate the limit.

Answer 1

Step 1:

The limit function is .

Using theorem :

If is integrable on , then .

Where .

The limit function is .

Here

But , then

.

Assume

Substitute in above expression.

.

Step 2:

Consider .

Graph :

This integration represents the area of the region under the curve and above axis in the interval .

 The area of the region in the interval is 0.346.  

Solution :

The area of the region under the curve from 0 to .