Question

express the area under the curve y=1/x from 2 to 4 as a limit with sample points chosen to be the midpoints of the corresponding segments. Do not evaluate the limit.

Answer 1

First, Draw a picture.

Answer 2

sorry its crappy

Answer 3

\[required area=\int\limits_{2}^{4}y dx=\int\limits_{2}^{4}\frac{ 1 }{ x }dx=2 \to 4 \left[ \ln x \right]=\ln 4-\ln 2=\ln \frac{ 4 }{ 2 }=\ln 2\]

Answer 4

is that the answer?

Answer 5

yes

Answer 6

thanks, but wat about the midpoints?

Answer 7

it is the area under the curve and between x=2 and x=4

Answer 8

got it thnks.

Answer 9

you are welcome.