Question

Help me explain?
See below.

Answer 1

\[\int\limits_{4}^{9} \sqrt{x} dx\]
n=8

Answer 2

i don't get this. i got rad37/8, but i didn't get 21/4

Answer 3

anti derivative of \(x^{\frac{1}{2}}\) is \[\frac{2}{3}x^{\frac{3}{2}}\]

Answer 4

it is the power rule in reverse

Answer 5

i know, but we're not using antiderivative. it's trapezoid rule.

Answer 6

then get rid of the exponential notation and write it as
\[\frac{2\sqrt{x}^3}{3}\]

Answer 7

trapezoid rule doesnt use antiderivative?
i know how to get the exact value of the integral...
but we're doing trapezoid rule right now...

Answer 8

ok, i guess that is what you have to do
looks like you are told to divide the interval in to 16 parts, each with length \(\frac{5}{16}\)

Answer 9

yeah i got that part.
i know the first one is rad (4+5/8), but how did they get rad(21/4)?

Answer 10

then i am lost because it looks like you have 8 terms instead of 16
damn

Answer 11

i think it includes the endpoints

Answer 12

oooh my fault
it is not a reimann sum, it is "trapazoid" which i don't really recall, but you can read about it here
http://www.mathwords.com/t/trapezoid_rule.htm

Answer 13

i know how to do it, but i just don't understand how they got rad(21/4) for the third term. and so on.

Answer 14

that will explain the 2 in each term, and also the fact that if \(\Delta x=\frac{5}{8}\) then you use \(\frac{\Delta x}{2}=\frac{5}{16}\) which is why you have 8 terms and not 16

Answer 15

ok i think i got it

Answer 16

you start at \(4\) and \(\Delta x=\frac{5}{8}\) so \(x_1=4+\frac{5}{8}=\frac{37}{8}\) and therefore \(f(x_1)=\sqrt{\frac{37}{8}}\)

Answer 17

i got that.

Answer 18

ok now what?

Answer 19

the second u would be rad(4+6/8)?

Answer 20

you add \(\Delta x\) each time, so next one is \(4+\frac{10}{8}\)

Answer 21

you don't increase the numerator by 1 each time, you move over \(\Delta x\) each time

Answer 22

\(x_1=4+\Delta x\), \(x_2=4+2\Delta x \), \(x_3=4+3\Delta x\) and so on

Answer 23

that should work, right?

Answer 24

@satellite73 can you please help me here!? i desperately need it! The population (in millions) of a certain country can be approximated by the function: P(x)=50*1.02^x where x is the number of years after 2000. Which of the following calculations will tell in what year the population can be expected to reach 100 million? a. ln(2/1.02)+2000 b. ln(2)/ln(1.02)+2000 c. ln(2/1.02) d. ln(2)/ln(1.02)

Answer 25

@erin512 repost and i will answer it

Answer 26

thanks!!

Answer 27

just reposted

Answer 28

........

Answer 29

@jennychan12 you got it?

Answer 30

\(x_2=4+2\Delta x=4+2\times \frac{5}{8}=\frac{21}{4}\)

Answer 31

yeah. do you always have to add by delta x?

Answer 32

yes, you divide the interval up in to \(n\) parts, each of which has length \(\Delta x=\frac{b-a}{n}\) so if you want to evaluate at the endpoint of the interval, you have go over \(\Delta x\) each time

Answer 33

i guess by "go over' i mean add

Answer 34

:o
i didn't add delta x for the previous problems that i did and i got the answer...