It is also called as path integral, contour or curve integral. The function to be integrated is evaluated along the curve. The value of the line integral is the sum of values at all points on the curve. Line Integrals are mostly used in Physics.
Example 1: If ∫ xy²ds c is the right half of the circle x² + y² = 9.
x = 3cost y = 3sint
x⁄3 = cost y⁄3 = sint
Let p = sint If t = -π⁄2 to π⁄2 then p = -1 to 1
dp= cost .dt
= 21(2) = 42