Calculating Integral of x^2-2x e^-x dx

In summary, an integral is a mathematical concept used to calculate the total value of a function over a given range by finding the area under a curve. The process for calculating an integral involves finding the antiderivative of the function and evaluating it at the upper and lower limits of integration. The integral of x^2-2x e^-x dx is important because it can be used to calculate quantities in fields such as science and engineering. However, there are limitations to calculating integrals, as not all functions have an antiderivative that can be expressed in terms of elementary functions. In these cases, numerical methods can be used to approximate the integral. The integral of x^2-2x e^-x dx can be applied in real
  • #1
mattibo
7
1
integral (x^2 - 2x) e^-x dx

Im just wondering if there's a fast way to calculate this integral or is the only way to do it by parts twice. The prof didnt show any work in the solution and went right to the solution. Am I missing something obvious?
 
Last edited:
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  • #2
what is E?
 
  • #3
sutupidmath said:
what is E?

eulers number (e)
 
  • #4
I think your plan of using integration by parts is the way to go.
 

What is an integral?

An integral is a mathematical concept that represents the area under a curve. It is used to calculate the total value of a function over a given range.

What is the process for calculating an integral?

The process for calculating an integral involves finding the antiderivative of the given function and evaluating it at the upper and lower limits of integration. This is commonly done using integration techniques such as substitution, integration by parts, or trigonometric substitution.

Why is the integral of x^2-2x e^-x dx important?

The integral of x^2-2x e^-x dx is important because it represents the total value of the function over a given range. It can be used in various fields of science and engineering to calculate quantities such as displacement, velocity, and acceleration.

What are the limitations of calculating integrals?

One limitation of calculating integrals is that not all functions have an antiderivative that can be expressed in terms of elementary functions. In these cases, numerical methods such as the trapezoidal rule or Simpson's rule can be used to approximate the integral.

How can the integral of x^2-2x e^-x dx be applied in real life?

The integral of x^2-2x e^-x dx can be applied in real life in various ways. For example, it can be used in physics to calculate the work done by a variable force, or in economics to calculate the total revenue of a company. It can also be used in probability and statistics to calculate probabilities and expected values for continuous random variables.

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