- #1
bearn
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Tricks for Saving Money on Groceries
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SUMMARY
This discussion centers around the mathematical concepts of derivatives and antiderivatives, specifically addressing the integration of polynomial functions. Participants clarify that the integral of the function $\displaystyle \int \dfrac{3}{2}x^2 + 5x + C \, dx$ results in $\dfrac{x^3}{2} + \dfrac{5}{2}x^2 + Cx + K$, while emphasizing the importance of understanding the distinction between finding a derivative and an antiderivative. The conversation highlights the necessity of correctly applying integration rules to avoid confusion.
PREREQUISITES- Understanding of basic calculus concepts, including derivatives and integrals.
- Familiarity with polynomial functions and their properties.
- Knowledge of integration techniques and rules.
- Ability to interpret mathematical notation and expressions.
- Study the Fundamental Theorem of Calculus to grasp the relationship between derivatives and integrals.
- Practice solving integrals of polynomial functions, focusing on correct application of integration rules.
- Explore advanced integration techniques, such as integration by parts and substitution.
- Review common mistakes in calculus to improve accuracy in solving problems.
Students, educators, and anyone looking to deepen their understanding of calculus, particularly in the areas of differentiation and integration of polynomial functions.
- #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
- 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
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As skeeter first said, you went "the wrong way"- you found the derivative, not the integral. $\frac{d(\frac{3}{2}x^2+ 5x+ C)}{dx}= 3x+ 5$
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