Homework Sourse23 Use the fundamental theorem for line integrals to evaluat
2.3) Use the fundamental theorem for line integrals to evaluate the line integral intC
Solution
Since ? (y^2 - 3x^2) dx = xy^2 - x^3 + g(y) ? (2xy + 2) dy = xy^2 + 2y + h(x), we see that the potential function is xy^2 - x^3 + 2y + C. Thus, the Fundamental Theorem implies that ?c (y^2-3x^2) dx + (2xy+2) dy = ?c ?(xy^2 - x^3 + 2y) · dr = (xy^2 - x^3 + 2y) {for (x,y) = (2, 1) to (-1, 0)} = 1 - (-4) = 5.
