Compute the line integrals intc1 f middot dr and intc2 f, Mathematics

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Compute the line integrals intc1 f middot dr and intc2 f

Consider the vector field F = (x² + y², 3xy). Compute the line integrals ∫_{c_1} F · dr and ∫_{c_2} F · dr, where c₁ (t) = (t, t²) and c₂(t) = (t, t) for 0 ≤ t ≤ 1. Can you decide from your answers whether or not F is a gradient vector field? Why or why not?

Is F conservative?

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Mathematics: Compute the line integrals intc1 f middot dr and intc2 f

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Mathematics: Compute the line integrals intc1 f middot dr and intc2 f

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