- #1
bearn
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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
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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. $\frac{d(\frac{3}{2}x^2+ 5x+ C)}{dx}= 3x+ 5$
Hello!
I tried to calculate projections of curl using rotation of coordinate system but I encountered with following problem.
Given:
##rot_xA=\frac{\partial A_z}{\partial y}-\frac{\partial A_y}{\partial z}=0##
##rot_yA=\frac{\partial A_x}{\partial z}-\frac{\partial A_z}{\partial x}=1##
##rot_zA=\frac{\partial A_y}{\partial x}-\frac{\partial A_x}{\partial y}=0##
I rotated ##yz##-plane of this coordinate system by an angle ##45## degrees about ##x##-axis and used rotation matrix to...
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