1. The problem statement, all variables and given/known data Calculate the curvilinear integral ∫C (x2 + y2)ds where C is the line segment [0,0] → [3,4]. Then calculate the maximum M of x2 + y2 along the segment and verify that the inequality ∫C (x2 + y2)ds ≤ M*length(C) holds. 2. Relevant equations ds = (x'(t)2 + y'(t)2)½dt ∇f(x,y) = λ∇g(x,y) g(x,y) = 0 3. The attempt at a solution I parametrized the segment as C = (3t, 4t) , 0≤t≤1. So x'(t) = 3, y'(t) = 4 and ds = 5dt with the formula given above. After plugging in and factoring out the 5, the integral becomes: 5∫01(9t2 + 16t2)dt = 125/3. I then proceeded to calculate the maximum along the segment using lagrange multipliers: equating the partial derivatives of x2 + y2 with the partial derivatives of g, I got: 2x = λ4/3 2y=-λ The constraint given by the segment is: g(x,y) = 4/3x - y = 0 By solving this system of 3 unknowns, I got the point (0,0) which plugged into the original equation gives 0 and the inequality does not hold. Is my reasoning correct and did I just miscalculate something or am I doing some conceptual error?