Must-know area formulas: (1) Between y = $x^n$ and y = x^$\frac{1}{n}$ from 0 to 1: A = |$\frac{1}{n+1}$ - $\frac{n}{n+1}$| = $\frac{n-1}{(n+1)}$ for n > 1, which simplifies differently; specifically for y = $x^2$ and y = sqrt(x), A = 1/3. (2) Between $y^2$ = 4ax and $x^2$ = 4by: A = 16ab/3. (3) Triangle with vertices (x1,y1), (x2,y2), (x3,y3): A = $\frac{1}{2}$|x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|. (4) Area cut off from parabola $y^2$ = 4ax by the line lx + my + n = 0: if the line intersects at points with parameters t1, t2, then A = $\frac{2a}{3}$|t1 - t2|^3 * a. (5) Between y = $e^x$, x-axis, x = 0 to x = k: A = $e^k$ - 1.