Calendar: 1882-1883 Page 630

general literature and science 627 At any point of circle straight line is drawn making the same angle with fixed diameter of the circle that the tangent at the point does shew that the envelope is hypo- cycloid of four cusps What is meant by an integral Distinguish between definite and indefinite integral Illustrate your answer by reference to 2a ax x2 dx 10 Integrate JL ג sin2 χ cos χ sec2 log tan Jan- x2 tan χ 7Γ 11 Prove that sini χ cos χ dx cose-2 ar ρ ρ e1nP 7Γ 7Γ and evaluate sin3 cos8 ώ sin5 cos 6fc si 12 Evaluate Ι β log sin θάθ τχ- Jo τ cos co fife ο 42 ף CO fife and thence deduce 13 Prove that the centre of gravity of one loop of the curve cos η θ is at distance 7r 164מ cos 7r ft2 9ft2 from the origin rr