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

  • Thread starter AbsoluteZer0
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The indefinite integral is a function of the variable x, so to be more precise, let's write that indefinite integral as a function of x : y(x) = \int12x³ + 6x² + 9xThe right result is y(x) = 3x⁴ + 2x³ + 4.5x² + CTo find the constant C, you can use the boundary conditions : Since the integral of a function is the inverse operation of a derivative, you must write that: y(x) = \int12x³ + 6x² + 9x = [3x⁴ + 2x³ + 4.5x² + C
  • #1
AbsoluteZer0
125
1
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
[itex]\int[/itex][itex]\frac{dy}{dx}[/itex] = [itex]\int[/itex]12x3 + 6x2 + 9x (the boundaries being 1 and 2)
[itex]\int[/itex]dy = [itex]\int[/itex]12x3 + 6x2 + 9x
y = [itex]\int[/itex]12x3 + 6x2 + 9x
y = [itex]\frac{12x4}{4}[/itex] + [itex]\frac{6x3}{3}[/itex] + [itex]\frac{9x2}{2}[/itex]]
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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  • #2
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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FAQ: Solution to PDA: Solving 12x3 + 6x2 + 9x

What is the solution to the given polynomial?

The solution to 12x3 + 6x2 + 9x is not a single number, but rather a set of three possible solutions. This is because the polynomial is of degree 3, meaning it has three terms with an exponent on the variable. In order to find the solutions, you can use methods such as factoring, the quadratic formula, or graphing.

Can I use the quadratic formula to solve this polynomial?

No, the quadratic formula can only be used for polynomials with a degree of 2, meaning it has one term with an exponent on the variable. In this case, the polynomial has a degree of 3, so you would need to use a different method to find the solutions.

Is there a shortcut or trick to solving this polynomial?

There is no one-size-fits-all shortcut or trick for solving polynomials. However, some polynomials may have special patterns that make them easier to solve, such as a common factor or perfect square trinomial. It is important to understand the various methods for solving polynomials so that you can choose the most efficient one for each specific problem.

Can I use a calculator to solve this polynomial?

While a calculator can be a helpful tool in solving polynomials, it is important to understand the underlying concepts and methods involved in finding solutions. Simply inputting the polynomial into a calculator without understanding the steps may not be helpful in the long run.

How do I know if my solution is correct?

You can check your solution to a polynomial by plugging it back into the original equation. If it satisfies the equation and results in an equal value on both sides, then it is a valid solution. You can also graph the polynomial and see if the solution(s) lie on the curve. Additionally, you can use a calculator to approximate the solutions and compare them to your own calculations.

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