Exercises

Exercises for Lectures #12

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1-2. Evaluate the line integrals:

1. where AB is the arc of a parabola from point A(1,1) to the point B(2,4) .

2. where C is an arc of the first arch of the cycloid which arc runs in the direction of increasing parameter t.

3-6. Applying Green’s formula, evaluate

3. where C is the contour of a triangle (traced in the positive direction) with vertices at the points A(1,1), B(2,2) and C(1,3). Verify the result obtained by computing the integral directly.

4. where C is the circle traced counter-clockwise.

5. where C is the circle . Verify the result obtained by computing the integral directly.

6. where C is the ellipse . Verify the result obtained by computing the integral directly.