Solve the Integral of x - 2|x| from [-1,2] | Easy Step-by-Step Solution

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Homework Help Overview

The problem involves evaluating the integral of the function x - 2|x| over the interval from -1 to 2. Participants are exploring the implications of the absolute value in the integrand and how it affects the integration process.

Discussion Character

  • Exploratory, Assumption checking, Mixed

Approaches and Questions Raised

  • Some participants attempt to simplify the integral directly, while others suggest breaking it into separate integrals based on the behavior of the absolute value function across the defined intervals.

Discussion Status

There is an ongoing exploration of how to handle the absolute value in the integral. Some participants have provided insights into evaluating the integral piecewise, but there is no explicit consensus on the correct approach or final answer yet.

Contextual Notes

Participants are considering the behavior of the function across different intervals, particularly noting that the function appears to be negative throughout the range of integration. There may be confusion regarding the evaluation of the integral and the expected results.

Shaybay92
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Homework Statement



Integral[ x - 2|x|]dx from [-1,2]


The Attempt at a Solution



Wouldn't it become x^2/2 - 2x^2/2 so x^2/2 - x^2 and then -x^2/2?

So from [-1,2] it would just be

-((2^2)/2) - - ((-1)^2/2) which is -1.5 but the answer is -3.5...
 
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Wait, sorry this shouldn't be the issue because from my graph the whole function is negative anyway... any suggestions?
 
I can be wrong, but I would try

[tex]\int_{-1}^2f(x)dx = \int_{-1}^0f(x)dx + \int_{0}^2f(x)dx[/tex]
 
I agree with Borek. The idea is that you can eliminate the absolute values by looking at the integrand on [-1, 0] and on [0, 2].

If x <= 0, |x| = -x.
If x >= 0, |x| = x.
 

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