vault backup: 2025-04-01 09:53:23

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

@@ -87,4 +87,6 @@ Average = $\dfrac{1}{b-a} \int_a^b f(x)dx$
 1. Let $f$ be a continuous function on the closed interval $[a, b]$ and let $F$ be any antiderivative of $f$, then:
 $$\int_a^b f(x) dx = F(b) - F(a)$$
 2. Let $f$ be a continuous function on $[a, b]$ and let $x$ be a point in $[a, b]$.
-$$ F(x) = \int_a^x f(t)dt \Rightarrow F'(x) = f(x) $$
+$$ F(x) = \int_a^x f(t)dt \Rightarrow F'(x) = f(x) $$
+$$ \dfrac{d}{dx} \int_a^{g(x)} f(t) dt = f(g(x)) * g'(x)* $$
+$$ \dfrac{d}{dx} \int_2^{7x} \cos(t^2) dt = $$