5.3 Integration & Anti-derivatives
The Fundamental Theorem of Calculus
Question #1 (Easy): Evaluating the Integral Based on the Graph
This is a simple calculation and reasoning exercise where the Fundamental Theorem of Calculus is not
directly applied. However, it works as a foundation where the change in the area under the curve is
linked to the anti-derivative of the curve. This helps to better understand the theoretical concept of the
Fundamental Theorem of Calculus.
Let ( ) ∫ ( ) where the graph of is shown.
1) Evaluate ( ), ( ) and ( ).
2) Estimate ( ) for , and .
3) On what interval is increasing?
4) Where does have a maximum value?
5) Sketch a rough graph of .
1) At ( ) ∫ ( )