Thread: Upper and Lower Limits of interval for Riemann's Sum

So i tried to this question and got f(x) = 1 + x
upper estimate = 9
lower estimate = 6

wondering if i'm on the right path. thx!

Originally Posted by simba412

So i tried to this question and got f(x) = 1 + x
upper estimate = 9
lower estimate = 6

No.

The lower limit is

The upper limit is

ohhh so: lower = 3, upper = 3+3x?

Originally Posted by simba412

ohhh so: lower = 3, upper = 3+3x?

not quite ...



as Plato stated ...



the lower limit is 3, but the upper limit is not 3 + 3x

i thought the upper limit was (1+x)dx where dx = 3, therefore 3(1+x)???

oh wait... (1 + (3-0))3 = 12?

...

thanks for the graph. i think i got it! the lower limit represents, in this case, the area of the red rectange. the upper limit represents the the area of the triangle + rectange multiplied by 2 since we take the upper value of x therefore = 4x3 = 12