- #1
bearn
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MHB Tricks for Saving Money on Groceries
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The discussion centers around a misunderstanding of calculus concepts, specifically the difference between finding a derivative and an antiderivative. Participants clarify that the integral of the function 3x + 5 should yield (3/2)x^2 + 5x + C, not the incorrect expression provided. Emphasis is placed on correctly applying integration rules to avoid confusion. The conversation highlights the importance of understanding fundamental calculus principles. Accurate comprehension of derivatives and integrals is essential for solving related mathematical problems.
- #2
skeeter
- 1,103
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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
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Where is your answer based from? What rule, if there is?skeeter said:
- #4
skeeter
- 1,103
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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
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As skeeter first said, you went "the wrong way"- you found the derivative, not the integral. $\frac{d(\frac{3}{2}x^2+ 5x+ C)}{dx}= 3x+ 5$