Confused on Solving a Series Computation: Help Needed!

In summary, the conversation is about finding a series accurate to within 0.001 using integration. The suggestion is to get the Maclaurin series for e-x2 and multiply it by x2. The person is unsure of what to do with the expanded form of the series and is advised to integrate term by term. The error in this series is less than the first unused term.
  • #1
intervade
7
0
Ok it says I am to computer using a series accurate to within 0.001.
gif.latex?\int_{0}^{1}x^2e^{-x^2}.gif


I'm really not sure where to start. Do I integrate this first by parts? Or am I thinking about this too much? Could someone point me in the right direction please! Help would be much appreciated!
 
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  • #2
intervade said:
Ok it says I am to computer using a series accurate to within 0.001.
gif.latex?\int_{0}^{1}x^2e^{-x^2}.gif


I'm really not sure where to start. Do I integrate this first by parts? Or am I thinking about this too much? Could someone point me in the right direction please! Help would be much appreciated!
The key word is series here. Get the Maclaurin series for e-x2, and then multiply it by x2. Does that give you a place to start?
 
  • #3
Ok let me just make sure I'm on the right track..

34zkmzb.jpg


Is this correct to say?

sorry, my latex skills are bad.
 
  • #4
No, write the series in expanded form, not in closed form. Notice that because you have an alternating series, the error is less in absolute value than your first unused term.

Your LaTeX looks pretty good!
 
  • #5
Hmm I'm not exactly sure what to do with this still. How do I integrate an expanded form of a series?
 
  • #6
Term by term. This series converges pretty quickly, so you shouldn't need a whole lot of terms.
 

FAQ: Confused on Solving a Series Computation: Help Needed!

What is a series computation?

A series computation is a mathematical process that involves adding together a sequence of numbers, usually in a specific order or pattern, to find a sum or total value. It is commonly used to solve problems in algebra, calculus, and other branches of mathematics.

How do I know which numbers to add in a series computation?

The numbers to be added in a series computation are typically given in a specific order or pattern. Look for clues such as the sequence of numbers, the presence of a common difference or ratio, or the use of terms like "sum" or "total." It is important to carefully read the problem and understand the given information before attempting the computation.

Can I use a calculator for a series computation?

Yes, you can use a calculator for a series computation, but it is important to understand the steps involved in the computation and how to use the calculator properly. Some calculators have specific functions for series computations, so it is recommended to check the user manual or online resources for guidance.

What are some common mistakes to avoid in series computations?

One common mistake in series computations is adding or subtracting the wrong numbers. It is important to carefully follow the given order or pattern and double check the numbers before performing the computation. Another mistake is forgetting to include all the terms in the series, which can lead to an incorrect result. It is also important to be aware of any special rules or formulas for the specific type of series being computed.

How can I check my answer for a series computation?

You can check your answer for a series computation by using a different method to solve the problem, such as using a formula or calculating the series in the reverse order. You can also use a calculator to verify the result. It is always a good idea to double check your work to ensure accuracy.

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