vault backup: 2025-04-17 09:30:41

education/math/MATH1210 (calc 1)/Integrals.md

@@ -109,7 +109,7 @@ This theorem tells us that a continuous function on the closed interval will obt
 # U-Substitution
 When you see $dx$ or $du$ in a function, it can be thought of as roughly analogous to $\Delta x$, where the change in $x$ is infinitesimally small.
 
-Thinking back to derivatives, when solving for $\dfrac{dy}{dx}$, you're solving for the rate of change of $y$ (across an infinitely small distance) over the rate of change of $x$ (across an infinitely small i$nstance). Given that the *slope* of a line is described as $\dfrac{\text{rise}}{\text{run}}$, 
+Thinking back to derivatives, when solving for $\dfrac{dy}{dx}$, you're solving for the rate of change of $y$ (across an infinitely small distance) over the rate of change of $x$ (across an infinitely small instance). Given that the *slope* of a line is described as $\dfrac{\text{rise}}{\text{run}}$, we know that $\dfrac{dy}{dx}$ describes the slope of a line at a particular point.
 ## Formulas
 - $\int k {du} = ku + C$
 - $\int u^n du = \frac{1}{n+1}u^{n+1} + C$