Mathematics

Problem

Evaluate

\int_C \mathbf{F} \cdot d\mathbf{r}

for the vector field

\mathbf{F}(x, y) = 2xy\mathbf{i} + (x^2 + \sin y)\mathbf{j}

and the curve

C

shown. ![Figure showing two curves C. (a) A curve starting at (0, 0) and ending at (2, pi/2). (b) A closed curve starting and ending at (0, 0).](https://storage.googleapis.com/diraq-contents/homework-question-parsing/marker/20251231T133952Z/3299dfc9c2d842768c622bf60fe2f1a6/5a36d88d3904f3f2d386c7cf63fa5053_img.jpg)

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