Calendar: 1891-1892 Page 821

ciNgingering department CXXX111 THIRD YEAR integral Calculus If φ ρή be finite and continuous for all values of between and η positive integer and nh -a prov that the limit of Ι φ α φ α φ α 2k φ ύ when η is indefinitely increased is jr where φ ν is the differential coefficient of yjs with respect to Apply this method to shew that cos χ dx sin sin Obtain the following integrals fix Λ -י χ ν χ tan xdx si η 6axdx and Λ λ2 r2 η If φ denote 2זג dx then when is positive nc Φ --ד Φ Hence obtain that מ 7r η η 7Γ sin afo 2-מ η positive integer if η is an even Prove that the area between catenary two parallel ordinates and the directrix is proportional to the length of the arc The ellipse revolves round the axis of χ find the volume generated particle falls from rest at the cusp of smooth cycloid