Question

Can somone please help me.......
Estimate the area under
f(x)=12x^-1
From x=1 to x=3 using 4 rectangles and left hand sums.
What is the estimate

Answer 1

the left hand endpoints will be 1, 1,5, 2, 2.5
evaluate the function at those points, add that up, and multiply the whole thing by\(\frac{1}{2}\)

Answer 2

is the answer 11.5

Answer 3

is that correct

Answer 4

i have no idea, i didn't do it

Answer 5

can you do it

Answer 6

give me a second, i will do it in wolfram

Answer 7

ok thanks

Answer 8

https://www.wolframalpha.com/input/?i=%2812%2B12%2F12.5%2B12%2F2%2B12%2F2.5%29*.5

Answer 9

so then 11.88 is the answer

Answer 10

that is ehat i got, yes

Answer 11

ok can you help me answer the second half also Should the estimate be over or under the true estimate

Answer 12

since \(\frac{12}{x}\) is decreasing on that interval, and since you are taking the left hand endpoints (where the function is biggest) then it will be an over estimate

Answer 13

ok thanks