Help with Integration: θ/(θ+2) from x=0 to 1

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    Integration
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Discussion Overview

The discussion revolves around the integration of the function θ/(θ+2) from x=0 to 1, specifically in the context of a statistical problem. Participants seek clarification and assistance with the integration process.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant requests help with the integration of θ(θ+1)∫xθ(1-x)dx, expressing uncertainty about the steps involved.
  • Another participant suggests a simplification of the integrand, stating that (x^t)(1-x) can be expressed as (x^t) - (x^(t+1)), implying familiarity with the integration of (x^t).
  • A third participant reiterates the original request for assistance, reformulating the equation with θ replaced by t for clarity.
  • A later reply expresses gratitude for the assistance, indicating that the basic concepts are challenging for them.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the integration process, and the discussion remains unresolved regarding specific steps or methods to solve the integral.

Contextual Notes

The discussion lacks detailed mathematical steps and assumptions that may be necessary for a complete understanding of the integration process.

bpschn01
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Hi,

I am told that:
θ(θ+1)∫xθ(1-x)dx = θ/(θ+2)
∫ from x=0 to 1
Would someone be so kind as to show me how, or give me some tips.

This is a small part of a solution for a statistical problem I'm trying to understand.
Thank you ...
 
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(x^t)(1-x) = (x^t) - (x^(t+1))
You know how to integrate (x^t) , i suppose.
 
bpschn01 said:
Hi,

I am told that:
θ(θ+1)∫xθ(1-x)dx = θ/(θ+2)
∫ from x=0 to 1
Would someone be so kind as to show me how, or give me some tips.

This is a small part of a solution for a statistical problem I'm trying to understand.
Thank you ...
In more readable form, and with θ replaced by t, the equation is
$$ t(t + 1) \int_0^1 x^t(1 - x)dx = \frac{t}{t + 2}$$
 
Thanks JJacquelin! It's the simple stuff that gets me.
 

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