# Line Integral and Vector Calculus

Related Topics:
More Lessons Engineering Math

Math Worksheets

A series of free Engineering Mathematics video lessons.

Path integral (scalar line integral) from vector calculus
I discuss and solve an example involving a path integral (also known as a scalar line integral) from vector calculus. In particular, I integrate a given function over a helix in 3D-space, where the integration is with respect to arc length. Such concepts are seen in 2nd-year university mathematics and enjoy applications to engineering.
Line integral example in 3D-space
I discuss and solve an example involving a line integral of a vector field over a given curve. For this example, the parametrization of the curve is given. The method involves reducing the line integral to a simple ordinary integral. Such an example is seen in 2nd year university mathematics.
Line integral from vector calculus over a closed curve I present an example where I calculate the line integral of a given vector function over a closed curve. In particular, I the vector function is a $${\bf F}(x,y) := (-y/(x^2 + y^2), x/(x^2 + y^2)$$ and the closed curve is the unit circle, oriented in the anticlockwise direction. I solve the problem and discuss the significance of the line integral through the mention of specific applications to engineering and physics.
Line integral from vector calculus over a closed curve
I present an example where I calculate the line integral of a given vector function over a closed curve.. In particular, I the vector function is a $${\bf F}(x,y) := (-y/(x^2 + y^2), x/(x^2 + y^2)$$ and the closed curve is the unit circle, oriented in the anticlockwise direction.
I solve the problem and discuss the significance of the line integral through the mention of specific applications to engineering and physics.
Line integral example from Vector Calculus
I discuss and solve a simple problem that involves the evaluation of a line integral. This particular line integral is in the differential form. The method used to solve this problem is one that involves a simple substitution. Such an example is seen in 2nd-year university mathematics.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.