Fundamental Theorem
If F(x) = ∫ₐˣ f(t) dt, then F'(x) equals
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About This Question
- Subject
- mathematics
- Chapter
- integral calculus
- Topic
- fundamental theorem
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
f(x)
- Fundamental Theorem of Calculus (Part 1): This theorem states that differentiation and integration are inverse processes.
- Statement: If f is continuous on [a,b], then for any x in (a,b), the derivative of the accumulating area function F(x)=∫axf(t)dt is simply the function evaluated at the upper limit.
- Conclusion: dxd∫axf(t)dt=f(x).
This easy difficulty mathematics question is from the chapter integral calculus, covering the topic of fundamental theorem. It appeared in the 2025 exam.
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