Line Integral Calculator
Calculate scalar line integrals along a parametric curve using numerical integration. Enter f(x,y), the curve x(t), y(t), and the parameter limits.
Integral details
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Line integral formulas
∫C f ds = ∫ f(r(t))|r′(t)| dt
∫C f dx = ∫ f(x(t),y(t))x′(t) dt
∫C f dy = ∫ f(x(t),y(t))y′(t) dt
Frequently asked questions
What is a line integral?
A line integral adds values of a function along a curve instead of across a straight interval. It is widely used in calculus, physics, and vector analysis.
What does ds mean?
ds is a tiny element of arc length. For a parametric curve, ds = √((dx/dt)² + (dy/dt)²)dt.
Can this calculate vector field work integrals?
This version calculates scalar integrals and integrals with respect to dx or dy. A full vector field work integral can be formed by adding separate P dx and Q dy results.
Results are estimates generated locally in your browser using standard mathematical formulas. They are for informational and educational purposes only and are not a substitute for verification in coursework, examinations or professional contexts requiring certified accuracy. VisionVix accepts no liability for decisions based on this tool's output.
