Apply Greenโ€™s theorem and Solve the Problem

4.B] Apply Greenโ€™s theorem to evaluate โˆซc[(3๐‘ฅ โˆ’ 8๐‘ฆ2)๐‘‘๐‘ฅ + (4๐‘ฆ โˆ’ 6๐‘ฅ๐‘ฆ)๐‘‘๐‘ฆ] ๐ถ, where C is the boundary of the region bounded by ๐‘ฅ = 0, ๐‘ฆ = 0, ๐‘ฅ + ๐‘ฆ = 1

Answer:-

4.B] Apply Greenโ€™s theorem to evaluate โˆซc[(3๐‘ฅ โˆ’ 8๐‘ฆ2)๐‘‘๐‘ฅ + (4๐‘ฆ โˆ’ 6๐‘ฅ๐‘ฆ)๐‘‘๐‘ฆ] ๐ถ, where C is the boundary of the region bounded by ๐‘ฅ = 0, ๐‘ฆ = 0, ๐‘ฅ + ๐‘ฆ = 1

4.B] Apply Greenโ€™s theorem to evaluate โˆซc[(3๐‘ฅ โˆ’ 8๐‘ฆ2)๐‘‘๐‘ฅ + (4๐‘ฆ โˆ’ 6๐‘ฅ๐‘ฆ)๐‘‘๐‘ฆ] ๐ถ, where C is the boundary of the region bounded by ๐‘ฅ = 0, ๐‘ฆ = 0, ๐‘ฅ + ๐‘ฆ = 1

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