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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
 one year ago
 one year ago
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
 one year ago
 one year ago

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wioBest ResponseYou've already chosen the best response.0
You basically want to find the area of the three rectangles. Make sense?
 one year ago

tavale21Best ResponseYou've already chosen the best response.0
sort of? how would i find the area's ?
 one year ago

wioBest ResponseYou've already chosen the best response.0
Well, for one, what is the area of a rectangle?
 one year ago

wioBest ResponseYou've already chosen the best response.0
I'm talking about in the general sense
 one year ago

tavale21Best 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?
 one year ago

wioBest ResponseYou've already chosen the best response.0
Okay, I just wanted to say, the area of a rectangle is length times width.
 one year ago

wioBest ResponseYou've already chosen the best response.0
So our first task is to find the width of the rectangles.
 one year ago

wioBest 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
 one year ago

wioBest ResponseYou've already chosen the best response.0
So what is the width of each rectangle?
 one year ago

wioBest ResponseYou've already chosen the best response.0
That is the width of the entire interval, not the width of each subinterval/rectangle
 one year ago

tavale21Best ResponseYou've already chosen the best response.0
oh ok. I see now ba/n=1
 one year ago

wioBest ResponseYou've already chosen the best response.0
Now, to find the length of the interval is a bit tricky.
 one year ago

wioBest ResponseYou've already chosen the best response.0
We need to pick some x in each subinterval. The length is then f(x).
 one year ago

wioBest 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.
 one year ago

wioBest 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.
 one year ago

wioBest ResponseYou've already chosen the best response.0
So the first interval is \(1*f(1) = 1 * 1^3 = 1\)
 one year ago

wioBest ResponseYou've already chosen the best response.0
The second interval is between a+w and (a+w)+w
 one year ago

wioBest ResponseYou've already chosen the best response.0
So the highest point is a+w+w = 0+1+1 = 2
 one year ago

wioBest ResponseYou've already chosen the best response.0
So the second subinterval area is \(1*f(2) = 1*2^3=1*8=8\)
 one year ago

wioBest ResponseYou've already chosen the best response.0
Do you think you can do the third sub interval?
 one year ago

tavale21Best ResponseYou've already chosen the best response.0
can you tell me the steps sorry im not good at this?
 one year ago

wioBest 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.
 one year ago

wioBest 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?
 one year ago

tavale21Best ResponseYou've already chosen the best response.0
are we adding the last f(3) to 8
 one year ago

wioBest 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
 one year ago

wioBest 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.
 one year ago

tavale21Best 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!!!
 one year ago

wioBest 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)
 one year ago

wioBest ResponseYou've already chosen the best response.0
How do you understand how I'm getting them?
 one year ago

tavale21Best 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.
 one year ago

wioBest 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.
 one year ago
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