4rxo = 111 4r = 2 Example 5 3 the 2 axis. t3 Solution The curve cuts the x- axis at y=0 or t t3 3 0 , Hence t=0 or 3 or x=0 or x=3.   t t3 Eliminating t from x=t2 and  we have the Cartesian equation of the y t 3 curve, 2 2 2 2   since (d s)2 = (d x)2 + (d y)2 dt dt dt 2 2 = 2 ds dt 1   t 2 2 The required surface area = yds 3 t3 3 3 3 2t 3 0 3 3  = = 3 = Sqr units 2 6
= 4rxo 111 = 4r 2 Example 5 axis. Solution 2 t3 3 the The curve cuts the x- axis at y=0 or t t3 3  0 , Hence t=0 or t  3 or x=0 or x=3. Eliminating t from x=t2 and y  t t3 3 we have the Cartesian equation of the curve, 2 2 2 2   since (d s)2 = (d x)2 + (d y)2 dt dt dt 2 = 2 2 ds dt  1  t 2 The required surface area = 2 yds 3 t3 3 3 0 2t 3 3 = 2 6 =  3 3 = 3 Sqr units
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