Question

Define Trapezoid rule calculus

Answer 1

Draw trapezoids whose area is easily calculated.

Answer 2

im given an table of vlaues

Answer 3

Where you find the area under the curve by creating multiple trapezoids and calculating each area of the figures individually and then adding them up to get the total.

Answer 4

Ah took dat test anyways
1/2 (h) (b1+b2)

You divide the intervals (into how many they ask you for)

Answer 5

Suppose that f(2) = 4, and that the table below gives values of f' for x in the interval
[0, 12]
x 0 2 4 6 8 10 12
f'(x) −19 −21 −25 −28 −29 −28 −25

estimate f(8)

Answer 6

So, h = 2...

Answer 7

yes

Answer 8

f(2) = 4
What is the average slope from 2 to 4?

Answer 9

@tkhunny not to be rude or anything but it's not called an average slope cause you just subtract the x variables from the other one.

Answer 10

I am sorry if I came off rude, I didn't mean to.

Answer 11

You're not being rude. We are supplied with values of f'(x). We have little information concerning f(x). We need the average slope between 2 and 4.

Answer 12

Not really the average slope, but some sort of mean value, since \(f'(c) = \dfrac{f(b)-f(a)}{b-a}\) for SOME value of c in (a,b). We're assuming, if you like, that c = 1/2.

Answer 13

my computer was lagging, however i have gotten the average and im lost on which values to use so far i have \[4+\int\limits_{2}^{8} f'(x)d(x)\]

Answer 14

im stuck on what to do from here

Answer 15

\(\int_{a}^{c}g(x)\;dx = \int_{a}^{b}g(x)\;dx + \int_{b}^{c}g(x)\;dx\) for a < b < c

Answer 16

The assumption in the formula is c = a. Simple as that. It just leads to a different approximation.