Question

For the function whose values are given in the table below, the integral from zero to six of f of x, dx is approximated by a Riemann Sum using the value at the midpoint of each of three intervals with width 2.


x 0 1 2 3 4 5 6
f(x) 0 0.25 0.48 0.68 0.84 0.95 1


The approximation is:

Answer 1

https://i.gyazo.com/bb48c4df913a466b00bd4c62e5b627ff.png

Answer 2

@ganeshie8 this is similar to the one we just did, but how would I split the intervals?

Answer 3

3 intervals with width 2 :

[0-2]
[2-4]
[4-6]

Answer 4

Ok, but what would I do with those 3 intervals?

Answer 5

in each interval, multiply the "value of function at midpoint of interval" by the "width"

by doing that you get an approximation for area of the region under the curve

Answer 6

I got 3.6 for when I did it but I just wanted to make sure both my method and answer was right

Answer 7

could you show complete work

Answer 8

Well I did it on paper so it's hard to show you :/

Answer 9

Looks your answer is wrong.
lets do it again, it wont take much time.

Answer 10

Look at the table,
whats the value of function at midpoint in first interval ?

Answer 11

.25

Answer 12

right, so `0.25*2` gives an approximation for area under the curve that interval

Answer 13

And would use the same logic throughout

Answer 14

Yes

Answer 15

So (.25*2)+(.68*2)+(.95*2)=3.76

Answer 16

Looks perfect!