Integral of x^e - Solving the Problem

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    Integral
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Discussion Overview

The discussion revolves around the integral of the function (x^e + e^x) from 0 to 1, focusing on the integration of the term x^e, where e is the mathematical constant. Participants explore the application of integration techniques and the treatment of e as a constant.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion regarding the integral of x^e, indicating it is a problem they have not encountered before.
  • Another participant clarifies that e is a constant, suggesting that the power rule can be applied to integrate x^e.
  • A third participant provides the integral of x^e, stating it is equal to (1/(e+1))x^(e+1) + C.
  • A fourth participant reiterates that e is a constant and compares the integration of x^e to that of x^2, implying that the process is straightforward.
  • This participant also states that the integral of e^x is simply e^x, concluding that the integration can be completed easily.

Areas of Agreement / Disagreement

Participants generally agree on the treatment of e as a constant and the application of the power rule for integration. However, there is no consensus on the overall approach to solving the integral, and some uncertainty remains regarding the integration process.

Contextual Notes

Some participants do not explicitly detail the steps for integrating e^x, and there may be assumptions about the familiarity with integration techniques that are not stated.

tommyninetwo
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I'm practicing integrals right now and came up on a question I have not seen before nor can I find online.

Integral from 0 to 1 of (x^e + e^x) dx

I'm stumped on x^e.
 
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In the case of [itex]x^{e}[/itex], e is just a constant. The power rule can be used.
 
[tex]\int x^e dx= \frac{1}{e+ 1}x^{e+ 1}+ C[/tex]
 
[itex]\int_0^1 (x^e+e^x)dx[/itex]

Note that 'e' is just a constant. It has a finite value, right?
So integrating it is just like how you integrate [itex]x^2[/itex].

The integral of [itex]e^x=e^x[/itex]. And you're done.
 

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