Calculate the line integral ∫ (4x + 2y²)dy
where C' is the curve y = x³, starting from x = 0, y = 0, and ending at x = 1, y = 1. Hint: express everything in terms of y.
Evaluate ∫c F. dr
where F = (x+2y)i + (y− x)j, dr = dri+dyj, and C is the path from (1,5) to (2,8) along the straight line y = 3x + 2.