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1. The instantaneous velocity of some object is given by

2. Find the length of the curve given by

3. Find the length of the curve given by

4. Find the length of the curve given by

5. Find the length of the curve given by parametric equations

6. Find the length of the curve given in polar coordinates by

7. Consider the curve

Find the surface area of the surface obtained by revolving this curve about the

*y*-axis.

Hint

Answer

8. Consider the curve

Find the surface area of the surface obtained by revolving this curve about the

*x*-axis.

Hint

Answer

9. Find the center of mass of a homogeneous half-disc of radius

*R*.10. Find the center of mass of the homogeneous solid given by the equation

*x*^{2}+*y*^{2}≤*z*≤ 9.11. Consider the ball of radius

*R*with center at the origin. Assume that its density is given by Find the mass and the center of mass of its half (the dome) given by*ϱ*(*x*) = |*x*|.*x*≥ 0.12. Find the derivative

of the function*F*′13. Find the derivative

of the function*F*′- 14. Evaluate .

Hint

Answer

- 15. Evaluate .

Hint

Answer