Expert: Paul Klarreich - 6/21/2010

Question
Use Trapizoid Rules to estimate Integral of 1 to 0 of  551x^550 dx. Find the value of n such that the error  ETn > M(b-a)^3/12n^2

Can you guide me through this

I have no idea what to do here but we can also write  a preogram for it on computer

Answer
Questioner: Sam
Country: United States
Category: Calculus
Private: No
Subject: Calculus
Question: Use Trapizoid Rules to estimate Integral of 1 to 0 of  551x^550 dx. Find the value of n such that the error  ETn > M(b-a)^3/12n^2

Can you guide me through this

I have no idea what to do here but we can also write  a preogram for it on computer
.............................................
Do you really mean:

{0
|
}1

and not

{1
|
}0

??

No matter, really.  I will assume the latter.

You could really compute the integral, because:

{1
| 551x^550 dx =
}0

x^551, from 0 to 1 = 1.  Yes, 1.

But you can compute your approximation using a program.  (I don't like Excel for this, since you don't know your n.)

As to the error, there is a well-known error expression:
(b - a)^3
---------  f''(z)
12n^2

where  z is between a and b.

In this case,  a = 0,  b = 1, so it is:
     1
E = ------  551 * 550 * 549 z^548
   12n^2

Now take  z = 1 (worst case) and

    551 * 550 * 549
E = ----------------
       12n^2

Now just decide how small you want the error to be.