 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-2/13/b/i/solution

Parameterize the straight line by

r (t) = (t, t, t)^{T}

0 \leq t \leq 1

. Then

r^{'} = (1, 1, 1)^{T}

and the line integral becomes

\int_{0}^{1} [2 t^{2} + (μ + 1) t^{2} + (λ + 1) t^{2}] d t = \frac{λ + μ + 4}{3} .

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