Ask your own question, for FREE!
Mathematics 5 Online
OpenStudy (anonymous):

In general, for approximate integration: - left end-point approximation (left Riemann's Sum) gives an UNDERESTIMATE - right end-point approximation (right Riemann's Sum) gives an OVERESTIMATE - mid-point rule gives an UNDERESTIMATE. Is this correct?

OpenStudy (jamesj):

If the function is increasing and is increasing at an increasing rate (such as the second derivative is positive), then yes. But these statements are not universally true of Riemann integrable functions. For example, the constant function f(x) = 1. In the case, the Riemann sum approximations are all exact. Another example, y =1-x, integration from x=0 to 1. Then the left end point approximations are going to be high, the right end ones low, and the mid-points will be exact.

OpenStudy (anonymous):

Ok I understand. Thank you.

OpenStudy (anonymous):

@JamesJ Unfortunately, this function was increasing at an increasing rate and I said that the midpoint rule would give an underestimate, but this was wrong. Why?

OpenStudy (anonymous):

that function is increasing at a decreasing rate (concave down)

OpenStudy (jamesj):

exactly

OpenStudy (anonymous):

Makes sense. Thanks

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Latest Questions
laylasnii13: Who wanna write or make a song with me???
3 hours ago 0 Replies 0 Medals
kaelynw: art igg
2 hours ago 9 Replies 1 Medal
XShawtyX: Art
21 hours ago 6 Replies 0 Medals
Nina001: teach me how to draw or just tell me the basics
23 hours ago 2 Replies 1 Medal
XShawtyX: We doing another drawing gimme ideas to add to this
1 day ago 9 Replies 1 Medal
RAVEN69: What is x 3+y 3+z 3=k
1 day ago 20 Replies 1 Medal
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!