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  Item Reference: KCLCAL-1893-1894-848

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cxxvi FACULTY OF SCIENCE 13 If AB is fixed chord of circle ABC and QQ' is any diameter and if Ρ be the point of intersection of QA Q'B prove that the locus of Ρ is circle whose centre is at the pole of the chord AB 14 rod of constant length has its extremities moving on the'circumferences of two fixed circles of equal known radii Obtain equations sufficient to determine the locus of its middle point and indicate without performing them what operations you would perform on these equations in order to obtain the desired equation of the locus integral Calculus YEAR III 15 State the method of integrating by substitution and shew that it is valid Integrate by this method χ si a2 x2 Find xdx xdx dx six2 fi9 a2 b2 x2 י έ χ2 16 Prove that dx uv ίνd- dx dx dx Find tan xdx Λγ2 "1 r2 17 If be the equation to any curve shew that the area between any two radii inclined at angles α β to the initial line and the curve is β τ2άθ Find the area of the curve x2 y2 a4x2 18 If un ד- -- shew that cos χ η un Aun-1 Bun-2 sin Un-1 dx and obtain the values of and
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