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 ∫ ( ) , where and and
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 ∫s ( ) .
2) from the limit becomes in the integral since .
3) ( ) ( ) ( ) ̅ in the limit becomes general f