Question

I don't understand this: Find a definite integral for which http://media.apexlearning.com/Images/200901/26/09c6e40a-8e4e-4c0e-b728-b0bc7fbabd78.GIF is a right rectangle approximation

Answer 1

How would I go about this ???

Answer 2

I think you might try and write the sumand as a product of x*f(x) (for length*height), assuming your approximating a function f(x).

Answer 3

okay i m sorry but i don t know what that means. i m very frazzled uh

Answer 4

i know right hand would end with six right ?

Answer 5

Ya, I think 6 rectangles.

Answer 6

okay... uh

Answer 7

oh wait.. 5 rectangles

Answer 8

oh yeah from 1 to 6 that 5

Answer 9

like i understand that part but what i m confused about is the inside of the function

Answer 10

like does it represent the height of each rectangle?

Answer 11

I don't see it either, but it's gotta be in a length*height. both the length and height might depend on k.

Answer 12

i think it might be \[\sqrt[3]{x}+4x\]

Answer 13

for the function itself but i need
the interval its on

Answer 14

So \[\frac{1}{2}\left({\frac{k+4}{2}}^{1/3}+4\left(\frac{k+4}{2}\right)\right)=\Delta x*f(x)\]

Answer 15

Ok, try and write it as \[\Delta x*(x^{1/3}+4x)\]

Answer 16

alright and then what

Answer 17

could be the step size \[\Delta x = 1/2\] and the rest is the integrand

Answer 18

So then interval is from 1 to 3

Answer 19

\[f(k)=\left({\frac{k+4}{2}}^{1/3}+4\left(\frac{k+4}{2}\right)\right)\]

Answer 20

\[\int_1^3 f(k) \text{d}k\] maybe works

Answer 21

uh,,, that s not one the options ... but ghh

Answer 22

these are the options and i don t really want the answer i just want to understand the problem

Answer 23

i thought it might ve been d but like... that would only work if the interval was like [0,6] ???

Answer 24

BUT! with our calculation we take 6 steps of size 1/2, so cover 3 units

Answer 25

So 5-2=3, are limits of integration that work

Answer 26

and that is an option

Answer 27

The sum is the number of steps. not the labels at the start and end of the interval. Does that make sense?

Answer 28

Right right.. Yeah that makes sense

Answer 29

:), so if we are right and \[\Delta x = 1/2, f(x)=\sqrt[3]{x}+4(x), \text{ and } x= \frac{k+4}{2}\] then it works.

Answer 30

alright alright

Answer 31

\[\int_{x_s}^{x_e} f(x) \text{d}x\] where \[x_e-x_s = 1/2*6\]

Answer 32

yeah yeah alright

Answer 33

sorry for taking so long to reply i always have to triple check my answers

Answer 34

np. was it right? does it make sense?

Answer 35

Ahh yeah it was right !! thank you so much for your help !! i really appreciate it !!