Question

The Integral

Answer 1

one moment please.

Answer 2

please help me solve the following:
A. Left-hand approximation
B. Right-hand approximation
C. Trapezoidal approximation
D. Midpoint

Answer 3

someone please help!!!

Answer 4

I'd draw a graph, just a basic sketch, of the points, makes these a little easier to do

Answer 5

i drew the graph. i know i need to use the riemann's sum.

Answer 6

using rectangles

Answer 7

im having a hard time finding a function to plug in the intervals.

Answer 8

i know how to find the midpoint, left points, and right points, and what to do with them; but i dont know what to do with them since there's no equation.

Answer 9

This is why drawing a diagram helps - A. Left-hand approximation
B. Right-hand approximation

are just the areas of those rectangles

Answer 10

So base*height

Answer 11

So Area = base*height

Answer 12

oh! then when i find the areas, I just add all 4? (n=4)

Answer 13

haha, yes I know. but my teacher never said anything like that. she said we'd need an equation.

Answer 14

For the trapezoid one you need the rule, http://tutorial.math.lamar.edu/Classes/CalcII/ApproximatingDefIntegrals.aspx

http://tutorial.math.lamar.edu/Classes/CalcII/ApproximatingDefIntegrals_files/eq0018MP.gif
the Delta x is the... width iirc, and the f(x) would be the height

Answer 15

are there rules for the left and right approx?

Answer 16

i have another question: if n=4, then why are there 9 rectangles? to confuse me?

Answer 17

i only have to use the first four, correct?

Answer 18

You have to use 4, that cover the whole length along the x-axis.

The x goes from 0 to 120, so each rectangle has length 30.

The left/right hand is how you choose the height of the rectangle.

Answer 19

so any 4 would work? does it matter which ones?

Answer 20

i drew the graph. im using the first and last one, and 2 from the middle area- since we're approximating it would be best to have a range.

Answer 21

Yes, the rectangles go from 0 to 30, then 30 to 60, etc

The lefthand means your height is using the left point.

Like for 0 to 30, the height is where x=0. For 30 to 60, the height is where x=30.

Right hand means the height is where x=30 for 0 to 30, x=60 for 30 to 60etc

Answer 22

Midpoint just means the height is given by the midpoint, x=15, x=45 etc

Answer 23

YES! thank you! i completely understand, now!!! i'll get help for the trapezoidal one from a someone else tomorrow. i dont want to keep holding you! thank you and good night!

Answer 24

tomorrow at school i mean.

Answer 25

hey @agent0smith ! could you tell me what kind of porblem this is...?

Answer 26

It's not even a full question, and what does "main of h(x)" mean

Answer 27

I'd also post as a new question, not in here

Answer 28

okay thanks. i guess there was a typo.