5.2 Integration & Anti-derivatives
Question #2 (Easy): Expressing the Limit as the Definite Integral
By the definition of the definite integral, the limit expression is set equal to the definite integral
over the interval
is integrable on .
Therefore, direct correlation between the limit and definite integral is established:
1) Definite integral means the interval is fixed. Definite integral describes this as
2) from the limit becomes in the integral since .
in the limit becomes general function notation in the integral.
Convert the limit into a definite integral over the given interval.
1) The interval is set as , thus .
And the definite integral will start with
2) The above step already took care of converting into .
3) Then take from the limit and let .
a. This means
b. By definition the function notation means:
Therefore, converting the limit into definite integral over given interval is expressed as follows: