From dff0d3a1cb1fa92e62a6eadfe0c7b8975ebb0296 Mon Sep 17 00:00:00 2001 From: arc Date: Thu, 17 Apr 2025 10:15:42 -0600 Subject: [PATCH] vault backup: 2025-04-17 10:15:42 --- education/math/MATH1210 (calc 1)/Integrals.md | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/education/math/MATH1210 (calc 1)/Integrals.md b/education/math/MATH1210 (calc 1)/Integrals.md index 3c3e8c9..8faf5c3 100644 --- a/education/math/MATH1210 (calc 1)/Integrals.md +++ b/education/math/MATH1210 (calc 1)/Integrals.md @@ -220,4 +220,8 @@ Where the two lines intersect each other, you'll need to split the solution into # Rotating a Solid Formed from a Rotation of a Plane Region Similar to finding the area between two curves, the volume can be found by approximating with rectangles. -The area of each rectangle can be found by taking the \ No newline at end of file +The area of each slice can be found by taking the area of the inner circle ($\pi r^2$) and subtracting it from the bigger circle ($\pi R ^2$). The area of a washer (or cylinder) can be found with $\text{base} * \text{height}$, and the height of each subsection is $\Delta x$. + +The Riemann Sum definition is defined as follows: +$$ \lim_{x \to \infty} \sum_{i = 1}^n ((\pi\cdot(f(x_i))^2-\pi\cdot(g(x_i))^2)\Delta x$$ +- $\Delta x$: The width \ No newline at end of file