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Evaluate integral C (y^2 + 1) dx + 2xy dy;

(a) C is the straight line from (-1; 0) to (1; 0).
(b) C is the arc of the circle x^2 + y^2 = 1 going counter-clockwise from (-1; 0) to (1; 0).

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Solution Summary

This provides an example of evaluating an integral as a straight line or as an arc.

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(a) the curve is parametrized by x = -1 + 2t and y = 0, with 0 =< t =< 1, in which case dx = 2 dt and dy = 0; hence the integral becomes

int_{0, 1} (0 + 1) (2 dt) = 2 ...

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