diff --git a/education/math/MATH1210 (calc 1)/Integrals.md b/education/math/MATH1210 (calc 1)/Integrals.md index b4da706..e0210c8 100644 --- a/education/math/MATH1210 (calc 1)/Integrals.md +++ b/education/math/MATH1210 (calc 1)/Integrals.md @@ -89,5 +89,10 @@ $$\int_a^b f(x) dx = F(b) - F(a)$$ 2. Let $f$ be a continuous function on $[a, b]$ and let $x$ be a point in $[a, b]$. $$ F(x) = \int_a^x f(t)dt \Rightarrow F'(x) = f(x) $$ $$ \dfrac{d}{dx} \int_a^{g(x)} f(t) dt = f(g(x)) * g'(x)* $$ +## Examples +> Finding the derivative of an integral $$ \dfrac{d}{dx} \int_2^{7x} \cos(t^2) dt = cos((7x)^2) * 7 = 7\cos(49x^2)$$ -$$ \dfrac{d}{dx}\int_0^{\ln{x}}\tan(t) = \tan(\ln(x))*\dfrac{1}{x} $$ \ No newline at end of file +> 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 +$$ F(x) = \int_4^x 2t \space dt = t^2 \Big|_4^x = x^2 - 16$$