A curve is defined by the parametric eqns x = t³ and y = 1 / (1 + t²). Sketch the curve for -2 ≤ t ≤ 2. Show that the region R bounded by the axes, the curve and the line x = a³, where a > 0 is given by ∫ª۪ √[3t²/(1+t²)] dt. Hence find the exact area of region S which is bounded by the y-axis, the curve and the line y = 0.5x. Find also the volume of the solid of revolution formed when S is rotated through 4 right angle about the y-axis, giving your answer corrected to 2dp.
Tags: