fundamental theorem

Question

If F(x) = ∫ₐˣ f(t) dt, then F'(x) equals

RankGuru · Accepted Answer

1. **Fundamental Theorem of Calculus (Part 1)**: This theorem states that differentiation and integration are inverse processes.
2. **Statement**: If $f$ is continuous on $[a, b]$, then for any $x$ in $(a, b)$, the derivative of the accumulating area function $F(x) = \int_a^x f(t) dt$ is simply the function evaluated at the upper limit.
3. **Conclusion**: $\frac{d}{dx} \int_a^x f(t) dt = f(x)$.

Rank Guru

fundamental theorem

Select the correct option: