Compute the lower Riemann sum for the given function f(x) = 3x over the interval [0, 1] with respect to the partition P = [0, 2/9, 8/9, 1]

Could someone explain how to do these? I missed class one day and now I'm lost.

Question

Compute the lower Riemann sum for the given function f(x) = 3x over the interval [0, 1] with respect to the partition P = [0, 2/9, 8/9, 1]

Could someone explain how to do these? I missed class one day and now I'm lost.

anonymous · Answer

for lowr Riemann sum, you'll need to use the left endpoint of the sub-intervals to get the height of each rectangle.

anonymous · Answer

Yes I know that part, what equation do I use to find the answer after that? is it distance[partition + partition + partition] or something like that? I'm trying to understand the notes from class but I don't know where she grabs some of these numbers

stamp · Answer

http://tutorial.math.lamar.edu/Classes/CalcI/AreaProblem.aspx

anonymous · Answer

there is no equation really... you're just adding the areas of 3 rectangles.

anonymous · Answer

How do I get the height of the rectangles? I guess the width would be the distance between the intervals but I don't know how to get height. Would it be f(intervalpartition)? like f(0)* distance from 0 to 2/9 == the area of the first rectangle?