The easiest way to guarantee an accurate integral calculation for these line integrals is to treat df as a positive displacement along the path. Where dy, dz > 0 and to have the limits of integration reflect the direction of travel for the integral along the path. Assume you have charge +q fixed at the origin and you bring in a charge 4 in from infinity to a distance away from the charge fixed at the origin along the x-axis. (a) Argue that the -dW work done by the +4 on the charge at all points of the path is dW. (b) Calculate this work using the dx notation above and using the appropriate integration limits and show that it produces the expected result: Remember that the electric field E points in the +x direction. (c) Imagine you wanted to define dx for this problem (to match the motion of the particle). What adjustments to the integration limits would you have to make in order to get the correct result of positive work on the negative particle?