- #1
bearn
- 11
- 0
Tricks for Saving Money on Groceries
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Discussion Overview
The discussion revolves around the concepts of integration and differentiation in calculus, specifically focusing on the antiderivative and its relationship to the derivative. Participants are examining a mathematical expression and clarifying the correct identification of derivatives versus antiderivatives.
Discussion Character
- Technical explanation
Main Points Raised
- Some participants assert that a previous response incorrectly identified an antiderivative as a derivative, emphasizing the need to distinguish between the two processes.
- One participant suggests an alternative expression for the integral, proposing that it should be $\displaystyle \int 3x+5 \, dx = \dfrac{3}{2}x^2 + 5x + C$.
- Another participant reinforces the idea that the original claim was incorrect by stating that the derivative of the proposed antiderivative yields the original function.
Areas of Agreement / Disagreement
Participants generally agree that there was a misunderstanding regarding the identification of derivatives and antiderivatives, but the specific details and interpretations remain contested.
Contextual Notes
There are unresolved assumptions regarding the definitions of the functions involved and the rules applied in the differentiation and integration processes.
- #2
skeeter
- 1,103
- 1
no ... you found the derivative, not the antiderivative.
$\displaystyle \int \dfrac{3}{2}x^2 + 5x + C \, dx = \dfrac{x^3}{2} + \dfrac{5}{2}x^2 + Cx + K$
$\displaystyle \int \dfrac{3}{2}x^2 + 5x + C \, dx = \dfrac{x^3}{2} + \dfrac{5}{2}x^2 + Cx + K$
- #3
bearn
- 11
- 0
Where is your answer based from? What rule, if there is?skeeter said:
- #4
skeeter
- 1,103
- 1
Maybe you meant ...
$\displaystyle \int 3x+5 \, dx = \dfrac{3}{2}x^2 + 5x + C$ ?
in any case, watch the video
$\displaystyle \int 3x+5 \, dx = \dfrac{3}{2}x^2 + 5x + C$ ?
in any case, watch the video
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- #5
Kansas Boy
- 44
- 0
As skeeter first said, you went "the wrong way"- you found the derivative, not the integral. $\frac{d(\frac{3}{2}x^2+ 5x+ C)}{dx}= 3x+ 5$
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