# 5.1 Integration & Anti-derivatives Area Estimate Under a Function Question #5 (Medium)

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5.1 Integration & Anti-derivatives

Area Estimate Under a Function

Question #5 (Medium): Interpreting the Limit

Strategy

This is same as Question #4 but working backwards.

Based on the limit expression:

1) Determine the interval from

2) Convert into a regular function notation without the subscript .

Sample Question

Find the functional region whose area is equal to the limit.

Solution

1) It looks like

, and since ,

fits the form of . So must be .

2)

and since , then

, which means so .

So the interval is , ie.

3) Since

, then

Therefore, the limit

represents the area under the function over the

interval (ie. .