A community for students.
Here's the question you clicked on:
 0 viewing
MistaGrimm
 4 years ago
how do i find the finite approximation to estimate the area using the lower sum of 4 rectangles for f(x)= 4x^2 between x=2 and x=2?
MistaGrimm
 4 years ago
how do i find the finite approximation to estimate the area using the lower sum of 4 rectangles for f(x)= 4x^2 between x=2 and x=2?

This Question is Closed

heisenberg
 4 years ago
Best ResponseYou've already chosen the best response.2well i see an easy way to make 4 rectangles from 2 to 2. they each have a width of 1.

heisenberg
 4 years ago
Best ResponseYou've already chosen the best response.2and they have a height of the minimum between f(x) and f(x+1), ie the left and right sides

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1i do not see a way to obtain a lower sum some of the rectangles end up above the curve starting from left endpoint or starting from right endpoint

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1i guess a lower sum does not mean all the rectangles have to be under the curve

heisenberg
 4 years ago
Best ResponseYou've already chosen the best response.2well the first rectangle would be from 2 to 1. f(2) = 0 f(1) = 2 this rectangle has 0 height, therefore it has no area. A = length * width = 0. second rectangle from 1 to 0 f(1) = 2 f(0) = 4 this rectangle has height of 2 (the minimum). area = height * width = 2 * 1 = 2 third rectangle from 0 to 1 is the same A3 = 2 fourth rectangle from 1 to 2 is the same as the first: A4 = 0 * 1 = 0 Total area = A1 + A2 + A3 + A4 = 4

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1starting from right endpoint we do Ar=1*(f(2)+f(1)+f(0)+f(1)] starting from left end point we do Al=1*(f(2)+f(1)+f(0)+f(1)]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1but these Ar=Al since f is even function

MistaGrimm
 4 years ago
Best ResponseYou've already chosen the best response.0sweet, thankyou both

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1oh wait Heisenberg i see i was only thinking of left endpoint rule and right endpoint rule and i even though of the mid point rule but we we could have chosen any number to approximate the area and since we want a lower sum we look in each of the intervals (2,1), (1,0), (0,1), (1,2) and pick the sample number that gives the minimum height great job Heisenberg

heisenberg
 4 years ago
Best ResponseYou've already chosen the best response.2ah yes. i didn't even think about those. luckily for me, it worked out. ...this time :p
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.