Is This Solution to the Integral and Series Problem Correct?

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Homework Help Overview

The discussion revolves around evaluating the integral of the function 3x²e^x and exploring the properties of a divergent series, specifically the harmonic series.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts integration by parts and presents their result for verification. They also inquire about the harmonic series as an example of a divergent series with terms approaching zero.

Discussion Status

Some participants provide feedback on the integral solution, with one suggesting differentiation as a verification method. The harmonic series is acknowledged as fitting the criteria mentioned by the original poster, but further exploration of its properties may be ongoing.

Contextual Notes

Participants are discussing the correctness of the integral solution and the nature of the harmonic series, with no explicit consensus reached on either topic.

bengaltiger14
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Homework Statement


Evaluate the integral 3x^2e^xdx



The Attempt at a Solution



I used integration by parts twice and came up with:

3x^2e^x-6xe^x+6e^x+C

Does that look correct.


Another question ask for a divergent series whose terms go to 0.
The harmonic series 1/n (with infinity on top of summation and n=1 on bottom) fits that criteria correct?
 
Physics news on Phys.org
1. google the integrator and check
2. yes you are correct
 
Even more simply, differentiate (3x2- 6x+ 6)ex+ C and see what you get!
 
Last edited:

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