Question

Please guide me c:
Find the area enclosed by the curves \(\sf y= \sqrt[3]{x}, y =1, y=2\ and x=0.\)

Answer 1

So first, i'm gonna draw a graph

Answer 2

thenn ?

Answer 3

Nice drawing. Great way to start. Going to divide this area into strips? If so, will they be vertical or horizontal, and why?

Answer 4

use horizontally simple better for taking the integral

Answer 5

xapproaches: why not let Data_LG2 answer that question, which was meant for him/her?

Answer 6

just suggest! of course he/she use whatever seen fit :)

Answer 7

it will be horizontal?


sorry, i had to refresh my browser.it is sticking.. brb

Answer 8

no it can be anything you want it was just a suggestion
try to use your own approach, wht you see better

Answer 9

\(\int\) f(x) - g(x) dx

This is what I would use for x=[1,8]
And for x=[0,1] it is a rectange.

Answer 10

Good choice. Having made that choice, how would you represent the length of a given horizontal strip algebraically?

Answer 11

now i'm back.

so if I'll use the horizontal, i have to do something like this:

\(\sf f(x) = \sqrt[3]{x}\) --> \(\sf x=f^{-1}(y)=y^3\) to make the integral easier to evaluate.... just thinking about using it, not really sure

Answer 12

my interval will be [1,2]

Answer 13

yep :)

Answer 14

you are going very well

Answer 15

Your strips are horiz., so you figure their lengths as the difference of two x values.
Consider how you'd represent those two x values.
Indicate which is the larger of the two.

Answer 16

Also consider: are you integrating with respect to x or to y?

Answer 17

with respect to y

Answer 18

Agreed. Because that's the case, your limits of integration, 1 to 2, are fine.

Answer 19

So, please write an expression for the AREA of a typical horiz. strip. What is the thickness of this strip? What is the length?

Answer 20

just visualizing the strips :)