Indefinite integrals. Arriving at different results.

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Start date May 12, 2012
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Indefinite Integrals

In summary, an indefinite integral is a mathematical concept used to find the family of antiderivatives of a given function. It differs from a definite integral in that it does not have specific limits of integration and therefore results in a general function rather than a numerical value. Different answers may be obtained due to the constant of integration and different methods used. To check for correctness, one can differentiate the result and use a graphing calculator. Tips for arriving at the correct result include practicing integration techniques, checking with differentiation, and paying attention to the constant of integration.

May 12, 2012

t6x3

*SOLVED* Indefinite integrals. Arriving at different results.

Mistake found. Thanks!, everything looks correct now.

Last edited: May 12, 2012

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May 12, 2012

Borek

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Integration constant is not a function of x.

May 12, 2012

arildno

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"(polynomial division 3x/x+3) ?(3)dx+4lnlx+3l + k =

My answer------> 3x+4lnlx+3l + k2

Your polynomial division is wrong.

1. What is an indefinite integral?

An indefinite integral is a mathematical concept that represents the family of all antiderivatives of a given function. It is denoted by ∫f(x)dx and is used to find the general solution of a differential equation.

2. How is an indefinite integral different from a definite integral?

An indefinite integral does not have any limits of integration, while a definite integral has specific upper and lower limits. This means that the result of an indefinite integral is a general function, while the result of a definite integral is a specific numerical value.

3. Why do indefinite integrals sometimes result in different answers?

Indefinite integrals may result in different answers due to the presence of a constant of integration, which can take on any value. This constant is usually represented by "C" and is added to the result of the integral. Different methods or techniques may also be used to solve the same integral, resulting in different answers.

4. How can I check if my indefinite integral is correct?

To check if an indefinite integral is correct, you can differentiate the result and see if it gives you the original function. If it does, then your integral is correct. It is also helpful to check your work using a graphing calculator or software.

5. Are there any tips for arriving at the correct result for indefinite integrals?

Some tips for arriving at the correct result for indefinite integrals include practicing various integration techniques, checking your work using differentiation, and using graphing software to visualize the function and its integral. It is also important to pay attention to the constant of integration and include it in your final answer.