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education/math/MATH1210 (calc 1)/Integrals.md
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@ -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 # 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. 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 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