diff --git a/education/math/MATH1210 (calc 1)/Integrals.md b/education/math/MATH1210 (calc 1)/Integrals.md index 63f05e9..26f685c 100644 --- a/education/math/MATH1210 (calc 1)/Integrals.md +++ b/education/math/MATH1210 (calc 1)/Integrals.md @@ -11,16 +11,18 @@ An antiderivative is useful when you know the rate of change, and you want to fi ## Formulas -| Differentiation Formula | Integration Formula | -| --------------------------------------------------- | ------------------------------------------------------- | -| $\dfrac{d}{dx} x^n = nx^{x-1}$ | $\int x^n dx = \dfrac{1}{n+1}x^{n+1}+ C$ for $n \ne -1$ | -| $\dfrac{d}{dx} kx = k$ | $\int k \space dx = kx + C$ | -| $\dfrac{d}{dx} \ln \|x\| = \dfrac{1}{x}$ | | -| $\dfrac{d}{dx} e^x = e^x$ | | -| $\dfrac{d}{dx} a^x = (\ln{a}) a^x$ | | -| $\dfrac{d}{dx} \sin x = \cos x$ | | -| $\dfrac{d}{dx} \cos x = -\sin x$ | | -| $\dfrac{d}{dx} \tan{x} = \sec^2 x$ | | -| $\dfrac{d}{dx} \sec x = \sec x \tan x$ | | -| $\dfrac{d}{dx} \sin^-1 x = \dfrac{1}{\sqrt{1-x^2}}$ | | -| $\dfrac{d}{dx} \tan^-1 x = \dfrac{} | | +| Differentiation Formula | Integration Formula | +| ----------------------------------------------------- | ------------------------------------------------------- | +| $\dfrac{d}{dx} x^n = nx^{x-1}$ | $\int x^n dx = \dfrac{1}{n+1}x^{n+1}+ C$ for $n \ne -1$ | +| $\dfrac{d}{dx} kx = k$ | $\int k \space dx = kx + C$ | +| $\dfrac{d}{dx} \ln \|x\| = \dfrac{1}{x}$ |
$\int \dfrac{1}{x}dx = \ln \|x\| + C$ | +| $\dfrac{d}{dx} e^x = e^x$ |
$\int e^x dx = e^x + C$ | +| $\dfrac{d}{dx} a^x = (\ln{a}) a^x$ | $\int a^xdx = \ln \|x\| + C$ | +| $\dfrac{d}{dx} \sin x = \cos x$ | $\int | +| $\dfrac{d}{dx} \cos x = -\sin x$ | | +| $\dfrac{d}{dx} \tan{x} = \sec^2 x$ | | +| $\dfrac{d}{dx} \sec x = \sec x \tan x$ | | +| $\dfrac{d}{dx} \sin^{-1} x = \dfrac{1}{\sqrt{1-x^2}}$ | | +| $\dfrac{d}{dx} \tan^{-1} x = \dfrac{1}{1+x^2}$ | | +| $\dfrac{d}{dx} k f(x) = k f'(x)$ | | +| $\dfrac{d}{dx} f(x) \pm g(x) = f'(x) \pm g'(x)$ | |