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tavale21
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approximate the area under each curve over the specified interval by using the indicated number of subintervals (or rectangles) and evaluating the function at the righthand endpoints of the subintervals.
f(x)=x^3 from x=0 to x=3; 3 subintervals
 2 years ago
 2 years ago
tavale21 Group Title
approximate the area under each curve over the specified interval by using the indicated number of subintervals (or rectangles) and evaluating the function at the righthand endpoints of the subintervals. f(x)=x^3 from x=0 to x=3; 3 subintervals
 2 years ago
 2 years ago

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wio Group TitleBest ResponseYou've already chosen the best response.0
dw:1353031457071:dw
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
You basically want to find the area of the three rectangles. Make sense?
 2 years ago

tavale21 Group TitleBest ResponseYou've already chosen the best response.0
sort of? how would i find the area's ?
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
Well, for one, what is the area of a rectangle?
 2 years ago

tavale21 Group TitleBest ResponseYou've already chosen the best response.0
is it from 0 to 3?
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
I'm talking about in the general sense
 2 years ago

tavale21 Group TitleBest ResponseYou've already chosen the best response.0
that's all that the book has. I looked at another problem and it is f(x) = 4xx^2 from x=0 to x=2; 2 subintervals and the answer was 7 square units. how did they get that?
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
Okay, I just wanted to say, the area of a rectangle is length times width.
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
So our first task is to find the width of the rectangles.
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
We will split up the interval equally into sub intervals... So we know with n subintervals on the interval [a,b], the width w is:\[ nw = ba \implies w=\frac{ba}{n} \]In this case, b = 3, a =0, and n = 3
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
So what is the width of each rectangle?
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
That is the width of the entire interval, not the width of each subinterval/rectangle
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
\[ \frac{30}{3} = 1 \]
 2 years ago

tavale21 Group TitleBest ResponseYou've already chosen the best response.0
oh ok. I see now ba/n=1
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
Now, to find the length of the interval is a bit tricky.
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
We need to pick some x in each subinterval. The length is then f(x).
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
But which x do we pick? It depends on the problem. This problem says that you want to pick the righthand endpoints, so we want to pick the x such that x is the highest value of x for that subinterval.
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
The first interval is from a to a+w, in this case 0 to 1. Since 1 is highest, right hand side, we use f(1) for the length of the interval.
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
So the first interval is \(1*f(1) = 1 * 1^3 = 1\)
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
The second interval is between a+w and (a+w)+w
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
So the highest point is a+w+w = 0+1+1 = 2
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
So the second subinterval area is \(1*f(2) = 1*2^3=1*8=8\)
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
Do you think you can do the third sub interval?
 2 years ago

tavale21 Group TitleBest ResponseYou've already chosen the best response.0
can you tell me the steps sorry im not good at this?
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
dw:1353032610122:dw
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
Okay, first step is to find with width of the rectangles. Next step is to find the length of each rectangle.
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
Then you add the areas of all the rectangles. Do you at least understand the high level idea of what we are doing?
 2 years ago

tavale21 Group TitleBest ResponseYou've already chosen the best response.0
are we adding the last f(3) to 8
 2 years ago

tavale21 Group TitleBest ResponseYou've already chosen the best response.0
the answer f(3) * 8
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
Nope. All I did was show that rectangle 1 has area 1, and rectangle 2 has area 8
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
So you need to find width times f(3) to find the area of rectangle 3. Then you add up the areas of all rectangles.
 2 years ago

tavale21 Group TitleBest ResponseYou've already chosen the best response.0
27+8+1= 36
 2 years ago

tavale21 Group TitleBest ResponseYou've already chosen the best response.0
can you explain how the left hand works? to the same problem? it makes sense now? thank you!!!
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
dw:1353033340267:dw
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
For the right hand, we use f(a+w), f(a+2w), f(a+3w), ... , f(a+(n1)w), f(a+nw) For the left hand, we use f(a), f(a+w), f(a+1w), ... , f(a+(n2)w), f(a+(n1)w)
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
How do you understand how I'm getting them?
 2 years ago

tavale21 Group TitleBest ResponseYou've already chosen the best response.0
from the picture you drawn up you use the rectangles starting from the left to the right.
 2 years ago

wio Group TitleBest ResponseYou've already chosen the best response.0
You will learn later, a method to do this with infinite subintervals. It's called a definite integral.
 2 years ago
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