Solution to PDA: Solving 12x3 + 6x2 + 9x

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SUMMARY

The discussion centers on solving the differential equation represented by the polynomial expression 12x³ + 6x² + 9x. The user correctly applies integration techniques, specifically the definite integral, to find the value of y over the boundaries of 1 and 2. However, a minor computational error occurs at the end of the calculation, and the notation used for functions and integrals is incorrect. Proper understanding of function notation and integral types is essential for accurate problem-solving in differential equations.

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This discussion is beneficial for students learning calculus, educators teaching differential equations, and anyone looking to improve their mathematical notation and integration skills.

AbsoluteZer0
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Hi,

I'm new to differential equations and I am wondering if I solved this one correctly or if it's entirely wrong. Is it a differential equation at all?

for

12x3 + 6x2 + 9x
\int\frac{dy}{dx} = \int12x3 + 6x2 + 9x (the boundaries being 1 and 2)
\intdy = \int12x3 + 6x2 + 9x
y = \int12x3 + 6x2 + 9x
y = \frac{12x<sup>4</sup>}{4} + \frac{6x<sup>3</sup>}{3} + \frac{9x<sup>2</sup>}{2}]
y = [3(2)4 + 2(2)3 + 4.5(2)2] - [3(1)4 + 2(1)3 + 4.5(1)2]
y = [48 + 16 + 18] - [9.5]
y = [76] - [9.5]
y = 66.5

Thanks,
 
Last edited:
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Hi !

The computation is almost entirely correct : only a mistake just at end.
But the writing of the symbols is almost entirely wrong (See attachment)
You have to take care of the different meanings and symbols of : Function, indefinite integral of the function and definite integral of the function.
 

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