query: Derivative/integral relationship appears to disprove the fundamental theorem of calculus!!!
positive_passages.docid: 149727
positive_passages.text: Fundamental Theorem of Calculus.
negative_passages.docid: 19828
negative_passages.text: Show that $\frac{x^3}{x^2+y^2}$ is not differentiable at $(0,0)$, even though all directional derivatives exist
negative_passages.docid: 56032
negative_passages.text: How come $\frac{1}{1-x}$ and $\frac{x}{1-x}$ have the same derivative?
negative_passages.docid: 131814
negative_passages.text: Integral with differential is purely imaginary
negative_passages.docid: 151127
negative_passages.text: Confirm that $\int_{0}^{\infty}t^{-1}\sin t dt=\pi/2$
negative_passages.docid: 48920
negative_passages.text: Mean value theorem for integrals: how does the sign matter?
negative_passages.docid: 117338
negative_passages.text: Counterexample to second derivative test when f''(x) is not continuously differentiable
negative_passages.docid: 107450
negative_passages.text: False proof that $ρe^{iθ} = ρ$ and so complex numbers do not exist?
negative_passages.docid: 99918
negative_passages.text: The $100$th derivative of $(x^2 + 1)/(x^3 - x)$
negative_passages.docid: 125324
negative_passages.text: Fundamental Theorem of Algebra - an elementary complex analysis proof?
negative_passages.docid: 32694
negative_passages.text: Prove that if a function $f$ has a jump at an interior point of the interval $[a,b]$ then it cannot be the derivative of any function.
negative_passages.docid: 125764
negative_passages.text: Under what conditions does Mathematica give a natural antiderivative when integrating?
negative_passages.docid: 119695
negative_passages.text: Understanding the relationship between differentiation and integration
negative_passages.docid: 124169
negative_passages.text: "What if" math joke: the derivative of $\ln(x)^e$
negative_passages.docid: 83022
negative_passages.text: Proof of this fairly obscure differentiation trick?
negative_passages.docid: 104510
negative_passages.text: For continuous $f$, $\int_0^x f(t)dt = ∫_x^1f(t)dt$ implies $f=0$.
negative_passages.docid: 88597
negative_passages.text: Improper integral from 1 to infinity $\Rightarrow$ integrated function converges towards zero?