7.7 Integral Techniques
Question #1 (Easy): Approximating the Integral Based on the Graph
Recall the approximate expression for five methods covered in the unit. Notice that no matter
which approximating method is used.
The given graph illustrate∫ ( ) .
1) Find and .
2) Find and .
3) Which ones of the 5 approximations are underestimates and
4) List these 5 approximations in increasing order.
The integral can be approximated as: ∫ ( )
All of them have . Since , then .
1) Since ∑ [ ( )] , so ∑ [ ( )] [ ( ) ( ) ( ) ( )]
[ ] [ ]
Since, ∑ [ ( ) ]