Finding line integrals -- please help! Given F = y/(x^2 + y^2) i - x / (x^2 + y^2) j Find the line integral of the tangential component of F from (-1,0) to (0,1) to (1,1) to (1,0) (assuming F is NOT path independent). --- I tried parameterizing each of the three paths using the formula r(t) = (1-t)r_0 + tr_1 --- I've been racking my brain on this for hours. The book says the answer is pi. My teacher says it isn't. For path 1: x = -1 + t, y = t => dx = dt = dy For path 2: x = t, y = 1 => dy = 0 For path 3: x = 1, y = 1-t => dx = 0 I then substituted these values in the original equation for F and integrated from t = 0 to t = 1 for each step. I get [tan^-1 (1) - tan^-1 (1)] + [tan^-1 (1) - tan^-1 (0)] + [tan^-1 (0) - tan^-1 (1)] = 0 + pi/4 - pi/4 = 0 Perhaps I take one of the tan^-1 (0) to be pi instead? What am I doing wrong? Please help!