Calendar: 1880-1881 Page 632

632 GENERAL LITERATURE AND SCIENCE 12 Write down three of the 'ultimate forms י from which other integrals are derived and define definite as dis- tinguished from an ζ indefinite integral 13 If χ and if the values a' and b' of ζ make equal to and respectively then dx dx ι φ χ dz a1 dz Apply this formula to integrate μ dx sec xdx a2 14 Explain the rule for integrating by parts Integrate and so reduce a2 x2 dx a2 dx that it may depend on this integral 15 How would you integrate such form as Jx Β ax2 2bx 16 Find formula of reduction for and hence shew that π 2sin30cosW0 gs XV ometrp anil &nalgttcat &eomtfrj Equal triangles which have one angle of the one equal to one angle of the other have their sides about the equal angles reciprocally proportional and prove the converse If ABC ADEbe two such triangles placed so that Β AE are in straight line and also CA AD and if BC DE produced meet in prove that FA will bisect CE and BB