Calc 1 Antiderivative Practice: Solving Complex Integrals for Final Exam

The key is to remember the basic rules of integration and to practice, practice, practice!In summary, the conversation is about a student seeking help with an antiderivative problem for their Calc 1 final exam. They were given a take-home quiz due to missed class time, but are struggling with one specific problem. The solution involves taking the integral of f'(x) and practicing basic integration rules.
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frumdogg
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Homework Statement



Hi everyone. My Calc 1 final exam is tomorrow and due to some weather related issues we were not able to cover all material for this quarter. With that said, my professor gave us a take home quiz on material that was unable to be covered. I have done by best, but I am getting hung up on an antiderivative problem.

Find the general antiderivative of:


f'(x) = 1-2x-4/[tex]\sqrt{x}[/tex]+5/x-8/(1+x^2)+9/x^4

Homework Equations



Now due to having virtually no time to learn about antiderivatives (we lost a whole week due to a blizzard and instructor illness) I am really unsure where to go. Do I need to rewrite the problem on one line and then find the opposite of the derivative?

Thanks!
 
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  • #2
Now due to having virtually no time to learn about antiderivatives (we lost a whole week due to a blizzard and instructor illness) I am really unsure where to go. Do I need to rewrite the problem on one line and then find the opposite of the derivative?

Thanks!

You take the integral of f'(x) to find the antiderivative. It will be in the form f(x) + C where f(x) is the antiderivative of f'(x).
 

1. What is a general antiderivative?

A general antiderivative, also known as an indefinite integral, is the reverse process of finding the original function that would result in a given derivative. In other words, it is the set of all possible functions whose derivative is the given function.

2. How is a general antiderivative different from a definite integral?

A definite integral has specific upper and lower limits, while a general antiderivative does not. This means that a definite integral will result in a single numerical value, while a general antiderivative will result in a set of functions.

3. What is the notation used for a general antiderivative?

The notation used for a general antiderivative is ∫f(x)dx, where f(x) is the function for which the antiderivative is being found and dx represents the variable of integration. The ∫ symbol is called the integral sign and is read as "the integral of."

4. How do you find a general antiderivative?

To find a general antiderivative, you can use a set of rules and formulas known as integration techniques. These include the power rule, substitution, integration by parts, and partial fractions. It is also important to remember to add a constant of integration (C) to the solution, as the derivative of a constant is always 0.

5. Why is finding a general antiderivative important?

Finding a general antiderivative is important because it allows us to solve a variety of real-world problems, such as calculating distances, areas, and volumes. It also plays a crucial role in advanced mathematical concepts and is essential for understanding the fundamental theorem of calculus.

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