i need help with finding upper and lower sums of the shaded region and the rectangles have the width of one. i have the graph, and i know b-a/n=4-0/4, which is one, but after that i am confused, i will try to post the graph, please help here is the graph http://assets.openstudy.com/updates/attachments/51566478e4b07077e0c033ef-moonlitfate-1364616709417-4.2_33.png

Question

zarkon · Answer

upper and lower sums for this function is just the right and left endpoints respectively

anonymous · Answer

its of the shaded region, and the rectangles have the width of 1

anonymous · Answer

hlep?

zarkon · Answer

what have you tried?

anonymous · Answer

i have tried $$\frac{ b-a }{ n }$$ which would be $$\frac{ 4-0 }{ 4 }$$
which is one, now when i get the main equation $$\sum_{i=1}^{n} f(mi)(Deltax) $$
which at theis point is get really confused, and the answers are 12.5 and 16.5 according to the back of the book

anonymous · Answer

?

zarkon · Answer

the function is increasing so the upper sum is just the right hand limits and the lower sums are the left hand limits

so for the upper since delta x =1  

we look at x=1,2,3,4  (that is where the max for f are located)

the y values are 3,4,4.5,5

add them up 3+4+4.5+5=16.5

zarkon · Answer

you really add them up and multiply by delta x.  but since delta x=1 we really don't have to worry about that

anonymous · Answer

ok that makes more sense thanks zarkon, continue to go where no man has gone before