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 2 years 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
 2 years 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

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

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

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

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

tavale21
 2 years ago
Best ResponseYou've already chosen the best response.0that'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?

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

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

wio
 2 years ago
Best ResponseYou've already chosen the best response.0We 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

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

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

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

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

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

wio
 2 years ago
Best ResponseYou've already chosen the best response.0But 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.

wio
 2 years ago
Best ResponseYou've already chosen the best response.0The 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.

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

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

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

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

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

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

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

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

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

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

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

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

wio
 2 years ago
Best ResponseYou've already chosen the best response.0For 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)

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

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

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