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anonymous
 one year ago
hey guys hope y"all are well so i have this advance level definite integral question which i have no clue how to slove help , appreciate it :)
https://fbcdnsphotosfa.akamaihd.net/hphotosakxfp1/v/t34.012/11909631_821736251278657_492814160_n.jpg?oh=3a6369ebefa89e9e8c6cabd375c6fabc&oe=55DC7BCA&__gda__=1440576288_0b59d00ed7b50754e40cf9942f4f8f3f
anonymous
 one year ago
hey guys hope y"all are well so i have this advance level definite integral question which i have no clue how to slove help , appreciate it :) https://fbcdnsphotosfa.akamaihd.net/hphotosakxfp1/v/t34.012/11909631_821736251278657_492814160_n.jpg?oh=3a6369ebefa89e9e8c6cabd375c6fabc&oe=55DC7BCA&__gda__=1440576288_0b59d00ed7b50754e40cf9942f4f8f3f

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freckles
 one year ago
Best ResponseYou've already chosen the best response.4\[\Delta x=\frac{ba}{N}\] this will be the base length of each rectangle

freckles
 one year ago
Best ResponseYou've already chosen the best response.4you will need to find the height formula... that is the distance from the curve to the xaxis is actually sqrt(x) the height is sqrt(x)

freckles
 one year ago
Best ResponseYou've already chosen the best response.4so starting at left endpoint you would do x=0 x=0+(ba)/N x=0+2(ba)/N x=0+3(ba)/N ... xi=0+i(ba)/N ... where i=0...35 this will give you 36 rectangles

freckles
 one year ago
Best ResponseYou've already chosen the best response.4right endpoint you would just use i=1..36 instead

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh wait from 1st rectangle to 36th rectangle ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.4\[A_\text{ \left endpoint rule }=\lim_{n \rightarrow \infty} \sum_{i=0}^{35} \Delta x \cdot f(a+i \frac{ba}{N}) \\ A_{\text{ \right endpoint rule }}=\lim_{n \rightarrow \infty} \sum_{i=1}^{36} \Delta x f(a+i \cdot \frac{ba}{N})\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thats the answer for a ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.4it can help you get to the answer though

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3dw:1440392239536:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.4lol i did 36 rectangles

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0See I do understand the definitions nd even can solve the question however I am struggling to understand what this question ultimately asking , I don't understand where U and L fit in the equation SRry about that

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes that's why I was confused why were u doing 36

freckles
 one year ago
Best ResponseYou've already chosen the best response.4now that will give you 18 rectangles

freckles
 one year ago
Best ResponseYou've already chosen the best response.4use i=0..17 for leftendpoint rule this will start your rectangles from x=0 use i=1..18 for rightendpoint tule this wil start your rectangles from x=0+(ba)/N

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3basically, the problem boils down to finding the area under the curve \(\large f(x)=\sqrt{~x}\) : dw:1440392648846:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3suppose you don't know calculus or anything, do you have any hope in finding the area of that blue region ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wait unless u know the size of each square

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3sure you know the size of each square

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3what riemann did is very simple : he divided that area into simple rectangles whose area can be found by simply multiplying width and height

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3we will see what U and L mean shortly, but just so you get used to this rectangles business, lets do a quick example maybe ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3can you find the area of below two big rectangles ? dw:1440393131543:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3notice that they both have same width : 18 you will need to find the height of each of them before using area of rectangle formula

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0When I saw the 18 I just did 18times 4

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.318 times 4 is 72, not 90

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3but from where did u get "4" ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0U said area together right ? So (4*9) +(6*9)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I just took approximation

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Ahh nice, you have the right idea, but your answer is wrong because the width of each rectangle is 18 dw:1440393575737:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3it seems you're assuming that the width of each rectangle is just 9, which is wrong..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Can I take the height of each rectangle 4 and 6

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3you may, but the exact heights are \(\sqrt{18}\) and \(\sqrt{36}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(4*18) + (6*16) = 168 unit^2

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3looks good! lets do one more exampl

freckles
 one year ago
Best ResponseYou've already chosen the best response.4dw:1440393845103:dw