Integration and taylor expansion

In summary, the conversation was about finding the integral of e^-2x * x^2 and the initial attempts using substitution and integration by parts. Eventually, it was suggested to start with integrating by parts, with u = x^2 and dv = e^-2x dx, which led to the solution of 1/4. Thanks to the help, the problem was solved.
  • #1
casanova2528
52
0
can anybody help me with this integration?

Integral of e to the -2x times x squared dx

it expands to 1/4, but I'm not sure how to start.
 
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  • #2
casanova2528 said:
can anybody help me with this integration?

Integral of e to the -2x times x squared dx

it expands to 1/4, but I'm not sure how to start.
Hey casanova, welcome to PF!

You don't really need a Taylor expansion here, how about trying a substitution?
 
  • #3
I have tried substitution

I've already tried substitution.

argh!

i've tried u = e ^ -2x

I've also tried u = x squared.

it doesn't work!

HELP!
 
  • #4
Integrate by parts and it works.
 
  • #5
start me off

with what do I start?
 
  • #6
casanova2528 said:
with what do I start?

you start by integrating

[tex]\int xe^{-2x}dx[/tex]

by parts.
 
  • #7
You integrate by parts. Start with x squared. You get

u = x^2
du = 2x dx

dv = e^-2x dx
v = -1/2 e^-2x

Give it a shot from there.
 
  • #8
thanks

i get it now...just needed a refresher...thanks a lot!
 

1. What is integration and why is it important?

Integration is a mathematical technique used to find the area under a curve. It is important because it allows us to solve real-world problems involving rates of change, distance, and many other physical quantities.

2. What is the difference between definite and indefinite integration?

Definite integration involves finding the exact numerical value of the area under a curve between two specified points. Indefinite integration, on the other hand, involves finding a general formula for the integral that can be used to find the value of the area at any point.

3. How does the Taylor expansion help in integration?

The Taylor expansion is a mathematical series that represents a function as an infinite sum of terms. It can be used to approximate the value of a function at a given point, which is helpful in integration as it allows us to solve integrals that cannot be solved using traditional methods.

4. Are there any limitations to using Taylor expansion in integration?

Yes, there are limitations. The Taylor expansion only provides an approximation of the function, so the more terms we include, the more accurate the approximation becomes. However, if we include too many terms, the calculation can become too complex and time-consuming.

5. Can integration and Taylor expansion be used in other fields besides mathematics?

Yes, integration and Taylor expansion have many applications in physics, engineering, economics, and other scientific fields. They can be used to solve problems involving rates of change, optimization, and many other real-world problems.

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