Path Integral Calculator
Calculate scalar path integrals along parametric curves in 2D.
Scalar Function f(x, y)
Use: x, y, ^, sin, cos, tan, exp, log, sqrt, pi
Parametric Path r(t)
Parameter Range
Path Integral Formula
integral_C f ds = integral_a^b f(r(t)) |r'(t)| dt
Path Integral
0.996392
integral_C f ds
LArc Length
1.478943
avgWeighted Avg
0.673719
minMin f
0.000000
maxMax f
1.997002
Path Endpoints
Start(0.0000, 0.0000)
End(1.0000, 1.0000)
Interpretation
- Weighted average: integral_C f ds / L = 0.6737
- Mass of wire with density f(x,y)
- Total accumulated quantity along path
About Path Integrals
Definition
A scalar path integral integrates a function along a curve with respect to arc length. It sums up the function values weighted by how far you travel along the path.
Applications
- Mass of curved wires with variable density
- Average temperature along a path
- Total distance with varying speed
- Center of mass of curves