Must-know area formulas: (1) Between y = x^n and y = x^(1/n) from 0 to 1: A = |1/(n+1) - n/(n+1)| = (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 = (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 = (2a/3)|t1 - t2|^3 * a. (5) Between y = e^x, x-axis, x = 0 to x = k: A = e^k - 1.