Engineering Mathematics|Important questions and solutions|BMATE201

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1. Using Green’s theorem evaluate ∮(𝑥𝑦 + 𝑦^2)𝑑𝑥 + 𝑥^2𝑑𝑦 over the region bounded by the curves 𝑦 = 𝑥 𝑎𝑛𝑑 𝑦 = 𝑥^2
2. Verify Stoke’s theorem for the vector field
𝑭 = (2𝑥 − 𝑦)𝑰 − 𝑦𝑧^2𝑱 − 𝑦^2𝑧𝑲 over the upper half surface of 𝑥^2 + 𝑦^2 + 𝑧^2 = 1, bounded by its projection on the 𝑥𝑦- plane.