Line integrals
Multivariable and vector calculus · Mathematics
Study notes
Q: Evaluate the line integral of (x + y) ds along the line from (0,0) to (1,1). Parametrize: r(t) = (t, t), 0 to 1. ds = sqrt((dx/dt)^2 + (dy/dt)^2) dt = sqrt(2) dt. Integrand: x + y = 2t. Integral = integral 0 to 1 of 2t sqrt(2) dt = sqrt(2) [t^2] 0 to 1 = sqrt(2).