Question

Find the circulation of the field f = x i y j around the curve r(t) = [cos(t)] i [sin(t)] j , 0 ≤ t ≤ 2π

Answer 1

The circulation of the field f = x i y j around the curve r(t) = [cos(t)] i [sin(t)] j is    2π ∫₀ (cos t sin t - sin t cos tj)dt = 0

Integration is described as blending matters or human beings collectively that have been formerly separated. An example of integration is while the schools have been desegregated and there have been now not separate public faculties for African individuals.

The method of finding integrals is referred to as integration. at the side of differentiation, integration is a fundamental, crucial operation of calculus, and serves as a device to solve troubles in mathematics and physics regarding the location of an arbitrary form, the length of a curve, and the extent of a solid, among others.

r (t) = cost i + sin t j = dr( sin ti + cos t)dt

F =  -xi -yj = -costi - sin tj

Flux = F .dr = $\int\limit2n^0_b {-costi - sin tj} \, dx$j)-( sin ti + cos t)dt

           $\int\limit2n^0_b {-costi - sin tj} \, dx$ -( sin ti + cos t)dt

     2π ∫₀ (cos t sin t - sin t cos tj)dt = 0

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