Calculus Volume 3 · free preview
Line Integrals
Line integrals accumulate a field's tangential component or a scalar's value along a curve, computing work and mass, parametrized by the curve's derivative and the element of arc length.
1. The scalar line integral
The scalar line integral
2. The vector line integral and work
The vector line integral and work
3. Properties and interpretations
Properties and interpretations
4. The fundamental theorem for line integrals
The fundamental theorem for line integrals
5. Scalar line integral element
The scalar line integral of f along C is computed with which element?
6. Vector line integral
The line integral of the vector field F along C equals which expression?
7. Circulation definition
The circulation of a vector field around a closed curve is which integral?
8. Rotation field circulation
The circulation of the rotation field (-y, x) around the unit circle equals what value?
9. Scalar versus vector line integrals
What distinguishes the scalar line integral from the vector line integral?
10. Arc length element parametrized
The arc length element ds equals |r prime of t| times what? Answer like dt.
11. Work energy theorem
The work done by a field equals the change in the particle's which quantity? Answer with two words.
12. Orientation reversal
Reversing the curve's orientation changes the vector line integral's sign. As a number, what factor? Answer with a number.
13. Conservative field line integral
For a conservative field F = gradient f, the line integral from A to B equals which difference?
14. Flux component
The flux across a plane curve uses which component of the field? Answer with two words.
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