Exercises

Exercises for Lectures #11

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1.-10. Evaluate the curvilinear integral of the second type along the given line (for non-closed curves direction of the bypass corresponds to increasing the parameter t or variable x; for closed curves direction is expected positive).

1. L– segment of a line from a point (0; 0) to (p; 2p).

2. L – arc of a line from a point (0; 0) to point (1; 1).

3. L – arc of a line from a point (0; 0) to point (1; 1).

4. L– arc of a circle

5. L – ellipse

6. L – arc of a circle

7. L – the line , xÎ [-1; 1].

8. L – the line y = 1 - |1-x|, xÎ [0; 2].

9. L– arc of a cycloid

10. L – the circle x2 + y2 = R2.