According to the Fundamental Theorem of Calculus, what do you get when you differentiate an integral?
Understand the Problem
The question asks about the Fundamental Theorem of Calculus and its implication when differentiating an integral. This theorem establishes a relationship between differentiation and integration, essentially stating that they are inverse processes of each other.
Answer
The original function.
According to the Fundamental Theorem of Calculus, differentiating an integral of a function gives you the original function back, provided the function is continuous.
Answer for screen readers
According to the Fundamental Theorem of Calculus, differentiating an integral of a function gives you the original function back, provided the function is continuous.
More Information
The Fundamental Theorem of Calculus has two parts. The first part states that differentiation and integration are inverse operations.
Tips
A common mistake is forgetting that the function must be continuous for the theorem to apply.
Sources
- Applying the fundamental theorem of calculus - khanacademy.org
- Fundamental theorem of calculus - Wikipedia - en.wikipedia.org
- 5.3: The Fundamental Theorem of Calculus Basics - Math LibreTexts - math.libretexts.org
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