The area of a polar curve is given by A=(1/2)∫ r2 d (theta). this can be interpreted as δA= ∏r2δ(theta)/2∏ (treating the area element as the area of a sector of a circle with angle δ(theta).) taking limit of δ(theta)→0, dA= [STRIKE]∏[/STRIKE]r2 d(theta)/2[STRIKE]∏[/STRIKE]=1/2 (r2d(theta) ) there fore A=1/2∫r2 d(theta). By the same logic, shouldn't length of a polar curve be L=∫[STRIKE]2∏[/STRIKE]r d(theta)/[STRIKE]2∏[/STRIKE]=∫r d(theta)? the actual equation for curve length is L=∫√(r2+r'2)d(theta). why is this approach giving me an incorrect equation in the second case but a correct one in the first? ps. the equation for length of a curve can also be derived by partially differentiating the equation for area by r: ∂A/∂r=L. This is again consistent with looking at length of a curve as the rate of change of area.