From 5463d89d1c7a0a3e98826ec446b5579697eec27b Mon Sep 17 00:00:00 2001 From: arc Date: Tue, 1 Apr 2025 10:08:23 -0600 Subject: [PATCH] vault backup: 2025-04-01 10:08:23 --- education/math/MATH1210 (calc 1)/Integrals.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/education/math/MATH1210 (calc 1)/Integrals.md b/education/math/MATH1210 (calc 1)/Integrals.md index e0210c8..063265c 100644 --- a/education/math/MATH1210 (calc 1)/Integrals.md +++ b/education/math/MATH1210 (calc 1)/Integrals.md @@ -94,5 +94,7 @@ $$ \dfrac{d}{dx} \int_a^{g(x)} f(t) dt = f(g(x)) * g'(x)* $$ $$ \dfrac{d}{dx} \int_2^{7x} \cos(t^2) dt = cos((7x)^2) * 7 = 7\cos(49x^2)$$ > Finding the derivative of an integral $$ \dfrac{d}{dx}\int_0^{\ln{x}}\tan(t) = \tan(\ln(x))*\dfrac{1}{x} $$ -> $x$ and $t$ notation +> $x$ and $t$ notation *(note: the bar notation is referred to as "evaluated at")* $$ F(x) = \int_4^x 2t \space dt = t^2 \Big|_4^x = x^2 - 16$$ +> $x$ in top and bottom +$$ \dfrac{d}{dx} \int_{2x}^{3x} \sin(t) dt = \dfrac{d}{dx} -\cos(t)\Big|_{2x}^{3x} = \dfrac{d}{dx} (-\cos(3x) + cos(2x) = 3\sin(3x) - 2\sin(2x) $$