Question

HELP!!! Urgently!!! Find the upper and lower sums of f(x) = -2x + 4 on the interval [0, 2] partitioned into four subintervals of equal length.

Answer 1

define the height of the rectangles at multiples of 2/4

Answer 2

I got that! But I don't know how to continue!

Answer 3

multily each value by the width ... 1/2

Answer 4

I'm confused!

Answer 5

-2(0/2) + 4
-2(1/2) + 4
-2(2/2) + 4
-2(3/2) + 4
-2(4/2) + 4


4
3
2
1
0

multiply by 1/2 gives us the area of the rectangles with those given heights

4/2
3/2
2/2
1/2
0/2

add the first 4, then add the last 4

Answer 6

But what would be the upper sum? and the lower sum?

Answer 7

as i posted ....

4/2
3/2
2/2
1/2
0/2

add the first 4, then add the last 4

Answer 8

I got 9.

Answer 9

4/2
3/2
2/2
1/2
----
10/2 = 5


3/2
2/2
1/2
0/2
-----
6/2 = 3

Answer 10

Yeah! I just realize that! Thank you so much! I really appreciate it! Thank you!

Answer 11

youre welcome

Answer 12

Another question, for this problem, "Estimate the area of the given function, f(x) = x2 + 1 using 4 inscribed rectangles on the interval [2, 4]," should I have to use the same method you just show me?

Answer 13

I figured it out! Thanks!