7.7 Integration Techniques
Integral Approximation: Overview
For integrals where algebraic evaluation of the anti-derivative is difficult or even impossible, various
approximation methods are used.
All approximation methods result in small amount of error so that if it were added to the approximation,
it equals the exact value of the integral.
Sample Point Approximation
∫ ( ) ∑ [ ( ) ] , where is any point in the th subinterval[ ]
If is chosen to be the left endpoint, then ( ) ∑ [ ( )]
If is chosen to be the right endpoint, then∫ ( ) ∑ [ ( ) ]
where for both, , and
∫ ( ) ∑ [ (̅) ] [ (̅̅̅ (̅̅̅ (̅̅̅)] , where , and ̅ is