Calendar: 1887-1888 Page 669

GENERAL LITERATURE AND SCIENCE 673 10 Evaluate the determinants and ו c2 c2 a2 a2 b2 III -BtfTtrutttal anfc integral Calculus Having given the rectangular equation of curve obtain an expression for the radius of curvature at any point χ χ If "J and that the radii of curvature at the points χ χ 2c are px p2 respectively prove that cP2 2p If the equation of curve is given by means of two equations connecting the rectangular coordinates with third variable prove that d6 expresses its area and explain how the limits are to be determined Apply this method to find the whole area of 3cos0 cos 30 sin sin 30 The curve Jχ -f Jy sja revolves round the axis of χ find the volume generated by the portion of the curve between the points where it touches the Shew how to integrate an equation of the form xy and trace the curve which exhibits the dx2 relation between and Apply the method of variation of parameters to obtain general form for the integral of Py where Pr dx are functions of ra 71 ז י Cut &l wf tri χ tיי יי Integrate cosec tan ן Prove that an integrating factor can always be found for the equation Μ Ν when Μ and iV are homoge- dx neous functions of χ and of the same degree υ υ