Line integrals and work practice problems
∫ F · dr along a path: parametrize, dot, integrate. 30 problems with worked solutions; in 30 of them every equation is proved by a computer algebra system.
Find the work done by \( \displaystyle \mathbf{F} = \langle x^{2}, x y \rangle \) along the unit circle, counterclockwise.
Find the work done by \( \displaystyle \mathbf{F} = \langle - y, x \rangle \) along the unit circle, counterclockwise.
Find the work done by \( \displaystyle \mathbf{F} = \langle y^{2}, 2 x \rangle \) along the line segment from (0, 0) to (1, 1).
Find the work done by \( \displaystyle \mathbf{F} = \langle y^{2}, 2 x \rangle \) along the parabola y = x² from (0, 0) to (1, 1).
Find the work done by \( \displaystyle \mathbf{F} = \langle - y, x \rangle \) along the parabola y = x² from (0, 0) to (1, 1).
Find the work done by \( \displaystyle \mathbf{F} = \langle y^{2}, 2 x \rangle \) along the line segment from (0, 0) to (2, 2).
Find the work done by \( \displaystyle \mathbf{F} = \langle x^{2}, x y \rangle \) along the parabola y = x² from (0, 0) to (1, 1).
Find the work done by \( \displaystyle \mathbf{F} = \langle - y, x \rangle \) along the line segment from (0, 0) to (2, 3).
Find the work done by \( \displaystyle \mathbf{F} = \langle y, x \rangle \) along the parabola y = x² from (0, 0) to (1, 1).
Find the work done by \( \displaystyle \mathbf{F} = \langle x + y, x - y \rangle \) along the parabola y = x² from (0, 0) to (1, 1).
Find the work done by \( \displaystyle \mathbf{F} = \langle y^{2}, 2 x \rangle \) along the line segment from (0, 0) to (1, 3).
Find the work done by \( \displaystyle \mathbf{F} = \langle x^{2}, x y \rangle \) along the line segment from (0, 0) to (2, 3).
Find the work done by \( \displaystyle \mathbf{F} = \langle y, x \rangle \) along the line segment from (0, 0) to (1, 3).
Find the work done by \( \displaystyle \mathbf{F} = \langle - y, x \rangle \) along the line segment from (0, 0) to (3, 2).
Find the work done by \( \displaystyle \mathbf{F} = \langle x + y, x - y \rangle \) along the unit circle, counterclockwise.
Find the work done by \( \displaystyle \mathbf{F} = \langle y^{2}, 2 x \rangle \) along the unit circle, counterclockwise.
Find the work done by \( \displaystyle \mathbf{F} = \langle x + y, x - y \rangle \) along the line segment from (0, 0) to (3, 2).
Find the work done by \( \displaystyle \mathbf{F} = \langle y, x \rangle \) along the line segment from (0, 0) to (3, 3).
Find the work done by \( \displaystyle \mathbf{F} = \langle x + y, x - y \rangle \) along the line segment from (0, 0) to (2, 2).
Find the work done by \( \displaystyle \mathbf{F} = \langle x^{2}, x y \rangle \) along the line segment from (0, 0) to (1, 3).
Find the work done by \( \displaystyle \mathbf{F} = \langle y, x \rangle \) along the unit circle, counterclockwise.
Find the work done by \( \displaystyle \mathbf{F} = \langle x^{2}, x y \rangle \) along the line segment from (0, 0) to (3, 3).
Find the work done by \( \displaystyle \mathbf{F} = \langle x + y, x - y \rangle \) along the line segment from (0, 0) to (3, 3).
Find the work done by \( \displaystyle \mathbf{F} = \langle x + y, x - y \rangle \) along the line segment from (0, 0) to (1, 3).
Find the work done by \( \displaystyle \mathbf{F} = \langle y, x \rangle \) along the line segment from (0, 0) to (1, 2).
Find the work done by \( \displaystyle \mathbf{F} = \langle x^{2}, x y \rangle \) along the line segment from (0, 0) to (2, 1).
Find the work done by \( \displaystyle \mathbf{F} = \langle - y, x \rangle \) along the line segment from (0, 0) to (1, 1).
Find the work done by \( \displaystyle \mathbf{F} = \langle x^{2}, x y \rangle \) along the line segment from (0, 0) to (2, 2).
Find the work done by \( \displaystyle \mathbf{F} = \langle y^{2}, 2 x \rangle \) along the line segment from (0, 0) to (3, 2).
Find the work done by \( \displaystyle \mathbf{F} = \langle y, x \rangle \) along the line segment from (0, 0) to (2, 3).