fix typos

quarto/integrals/area_between_curves.qmd

@@ -718,7 +718,7 @@ let
     O = (0, 0)
     x1, y1 = P = (2, 2)
     x2, y2 = Q = (1, 3)
-    plt = plot(; legend=false, aspect_ratio=:equal, framestyle=:orgin)
+    plt = plot(; legend=false, aspect_ratio=:equal, framestyle=:origin)
     plot!(plt, [O,P,Q,O]; line=(1, :black))
     scatter!(plt, [O, P, Q]; marker=(5, :black))
     annotate!(plt, [

quarto/integrals/center_of_mass.qmd

@@ -227,10 +227,10 @@ The bottom integral is just the area (or total mass if the $\rho$ were not cance
 ##### Example
 
 
-Find the center of mass formed by the intersection of the parabolas $y=1 - x^2$ and $y=(x-1)^2 - 2$. @fig-center-of-mass-of-two-parabola-1-minus-xsquared-and-x-minus-1-sqared-minus-2 shows that for the $x$ direction, it is close to $1/2$.
+Find the center of mass formed by the intersection of the parabolas $y=1 - x^2$ and $y=(x-1)^2 - 2$. @fig-center-of-mass-of-two-parabola-1-minus-xsquared-and-x-minus-1-squared-minus-2 shows that for the $x$ direction, it is close to $1/2$.
 
 
-::: {#fig-center-of-mass-of-two-parabola-1-minus-xsquared-and-x-minus-1-sqared-minus-2}
+::: {#fig-center-of-mass-of-two-parabola-1-minus-xsquared-and-x-minus-1-squared-minus-2}
 ```{julia}
 #| echo: false
 f1(x) = 1 - x^2

quarto/integrals/substitution.qmd

@@ -22,7 +22,7 @@ using SymPy
 
 The technique of $u$-[substitution](https://en.wikipedia.org/wiki/Integration_by_substitution) is derived from reversing the chain rule: $[f(g(x))]' = f'(g(x)) g'(x)$.
 
-::: {.definition title="Subsitution"}
+::: {.definition title="Substitution"}
 
 Suppose that $g$ is continuous and $u(x)$ is differentiable with $u'(x)$ being Riemann integrable. Then both these integrals are defined and are equal:
 

quarto/integrals/surface_area.qmd

@@ -668,7 +668,7 @@ f(t) = 2(1 + cos(t)) * sin(t)
 plot(g, f, 0, 1pi)
 ```
 
-Paremeterized curve to rotate about $x$ axis
+Parameterized curve to rotate about $x$ axis
 :::
 
 The integrand simplifies to $8\sqrt{2}\pi \sin(t) (1 + \cos(t))^{3/2}$. This lends itself to $u$-substitution with $u=\cos(t)$.