 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-2/13/a/i/solution

With

r (t) = (t, t^{2})^{T}

(1, 2 t)^{T}

and

F (r (t)) = (t^{3}, 2 t^{2})^{T}

\int_{0}^{1} (t^{3} + 4 t^{3}) d t = \frac{5}{4} .

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