User:Nathaniel Reindl/LaTeX Playground

My Shells Method
$$2\pi\int_{a}^{b} xy\,dx$$

$$2\pi\int_{a}^{b} yx\,dy$$

I write my initial setups this way because the relationship between the individual components of the problem are visually more apparent. It looks more like you're trying to find the area of a rectangle in the integrand (which is what you're doing with shells) instead of some blue-crack nonsense like $$x\,f(x)$$. That product doesn't intuitively look like you're finding the area of something.

SIUE Math 152 Shells Method (The Blue Crack Method)
$$2\pi\int_{a}^{b} xf(x)\,dx$$

$$2\pi\int_{a}^{b} yf(y)\,dy$$

Stupid Crap
$${{d}\over{d\,x}}\,\left(f\left(x\right)\,g\left(x\right)\right)=f \left(x\right)\,\left({{d}\over{d\,x}}\,g\left(x\right)\right)+g \left(x\right)\,\left({{d}\over{d\,x}}\,f\left(x\right)\right)$$