(Arc lengths, Exercises 7.3) Find the lengths of the given curves.
(a) y =
from x = 1 to x = 4.
(b) y = x2
from x = 1 to x = 2
(Surface area, Exercises 7.3)
(a) Find the area of the surface obtained by rotating y = sinx (0 lt; lt; lt; lt;)
about the r-axis.
(b) Find the surface area of the torus (doughnut) obtained by rotating the circle
(x – b)2 + y2 = a2 about the y-axis.Math