📚 Topic Summary
Finding functions from derivatives involves determining the original function given its derivative. This process is known as antidifferentiation or integration. The key concept is understanding that multiple functions can have the same derivative because the derivative of a constant is always zero. Therefore, when finding a function from its derivative, we must include a constant of integration, often represented as 'C'. Techniques like substitution and integration by parts are essential tools in this process. This printable activity provides practice in applying these concepts.
🧠 Part A: Vocabulary
Match the following terms with their definitions:
| Term |
Definition |
| 1. Derivative |
A. The reverse process of differentiation. |
| 2. Antiderivative |
B. A function whose derivative is the given function. |
| 3. Integration |
C. An operation that produces a family of functions. |
| 4. Constant of Integration |
D. The instantaneous rate of change of a function. |
| 5. Indefinite Integral |
E. A constant term added to the antiderivative to represent all possible solutions. |
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words provided:
(Derivative, Antiderivative, Integration, Constant, Function)
Finding the ________ of a function involves the process of ________. The result is an ________ which represents a family of functions differing by a ________. Therefore, it is crucial to remember to add 'C' after performing the ________. The original equation is called a ________
🤔 Part C: Critical Thinking
Explain why it's important to include '+ C' (the constant of integration) when finding a function from its derivative. What does '+ C' represent mathematically and graphically?