Is My Calculation of the Antiderivative Correct?

Thread starter rowdy3
Start date Apr 16, 2011
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Antiderivatives

In summary, an antiderivative is the inverse operation of a derivative and can be found using rules of integration such as the power rule, substitution, and integration by parts. To check if the antiderivative is correct, it can be differentiated and compared to the original function or a graphing calculator can be used. A constant, known as the constant of integration, can be included in an antiderivative without affecting the result when differentiated. Common mistakes to avoid when finding antiderivatives include forgetting the constant of integration, using the power rule incorrectly, and not applying the chain rule correctly. It is also important to watch out for algebraic errors and simplify the final answer.

Apr 16, 2011

rowdy3

Find the following.
∫ (56t^(5/2) + 18t^(7/2))dt.
I did
(2/7)56 t^(7/2) + (2/9)18t^(9/2) + c =
16t^(7/2) + 4t^(9/2) + c

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Apr 16, 2011

SammyS

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It looks good to me.

Check it by taking the derivative of 16t^(7/2) + 4t^(9/2) + C .

1. What is an antiderivative?

An antiderivative is the inverse operation of a derivative. It is a mathematical function that, when differentiated, produces the original function. It is also known as the indefinite integral.

2. How do I find an antiderivative?

To find an antiderivative, you must use the rules of integration. These include the power rule, substitution, and integration by parts. You can also use tables of integrals or computer software to find antiderivatives.

3. How do I know if I did the antiderivative correctly?

You can check your antiderivative by differentiating it. If the result is the original function, then you have done it correctly. You can also compare your answer with known antiderivatives or use a graphing calculator to verify your solution.

4. Can I have a constant in my antiderivative?

Yes, you can have a constant, also known as the constant of integration, in your antiderivative. This is because when you differentiate a constant, it becomes zero. So, adding a constant to your antiderivative does not change the result when differentiated.

5. Are there any common mistakes to avoid when finding antiderivatives?

Yes, there are a few common mistakes to avoid when finding antiderivatives. These include forgetting the constant of integration, using the power rule incorrectly, and not applying the chain rule correctly. It is also important to watch out for algebraic errors and to simplify your final answer as much as possible.