The antiderivative ofx*exp(1-x)

In summary, the antiderivative of x*e^(1-x) is given by the formula \int u dv = uv - \int v du, where u = x and dv = e^(1-x) dx. By differentiating u and integrating dv, you can find the values of u and v and plug them into the formula to find the antiderivative. It is recommended to use the homework posting template and post in the appropriate section for future questions.
  • #1
Broken_Mirage
3
0
pleasezz the antiderivative ofx*exp(1-x)

hi all,,,,,,



pleasezz the antiderivative ofx*exp(1-x)


tomorrow 11/1/2007 is the last day

please
 
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  • #2
You left it a bit late didn't you? Anyway, please provide your thoughts on a solution to the problem (for example, do you know any methods of integrating products?) Better still, in future, use the homework posting template with which you were provided!
 
  • #3
Well since you don't really have much time, Ill just get through to you the essentials, But can't give you the answer.

[tex]\int u dv= uv-\int v du[/tex]

Let u=x, dv= e^(1-x) dx. Differentiate u with respect to x, and take the dx to the other side to get du. Integrate dv to get v. Once you have those values, sub them into that equation and your done. Good Luck

EDIT: O btw this is obviously calculus, put this is the calculus section next time.
 

What is the antiderivative of x*exp(1-x)?

The antiderivative of x*exp(1-x) is (1-x)*exp(1-x) + C, where C is a constant of integration.

What is the process for finding the antiderivative of x*exp(1-x)?

To find the antiderivative of x*exp(1-x), you can use the u-substitution method. Let u = 1-x, then du = -dx. The integral then becomes -exp(u)du, which can be easily solved using integration by parts.

Can the antiderivative of x*exp(1-x) be simplified further?

Yes, the antiderivative of x*exp(1-x) can be simplified further by using properties of exponentials. For example, you can rewrite (1-x)*exp(1-x) as exp(1-x) - x*exp(1-x).

Is the antiderivative of x*exp(1-x) a single function or a family of functions?

The antiderivative of x*exp(1-x) is a family of functions, as it includes a constant of integration. This means that there are infinite possible antiderivatives for this function.

What are some real-world applications of the antiderivative of x*exp(1-x)?

The antiderivative of x*exp(1-x) has applications in many fields, including physics, engineering, and economics. For example, it can be used to model the rate of change of a population over time, the decay of radioactive materials, or the growth of investments with compound interest.

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