21.1  a) arc length x^(3/2)/3+1, x=0..2
         integral sqrt(1+x/4 )dx from 0 to 2
      b) arc length x^(3/2), x=0..4
         integral sqrt(1+9x/4 )dx from 0 to 4
      d) arc length x^3/6+1/(2x), x=2..3
         integral sqrt(1+1/4*(x^2-1/x^2)^2 )dx from 2 to 3
      e) arc length ln(sin(x)), x=1..pi/2
         integral 1/sin x dx from 1 to pi/2

21.3  ParametricPlot[{x=cos (theta),y=sin (theta)},{theta,-9/4pi,-5/4pi}]
      arc length x=cos(t), y=sin(t), t = -9/4pi..-5/4pi
	  integral r dx from -9/4pi to -5/4pi

21.4  ParametricPlot[{x=cos^3 (theta),y=sin^3 (theta)},{theta,0pi,2pi}]
      arc length x=cos(t)^3, y=sin(t)^3, t = 0..2*pi
      integral 3*|sin(x)*cos(x)| dx from 0 to 2pi

21.5  integral pi*(1-x^2)^2 dx from -1 to 1

21.6  integral 4*1/2*x^2 dx from 0 to 2

21.7  integral 1/2 * 3x/5 * 4x/5 dx from 0 to 5

21.8  c) plot[{x^2+1,x+1},{x,0,1}]
         integral pi * ((x+1)^2-(1+x^2)^2) dx from 0 to 1
      e) plot[{cos x},{x,0,pi}]
         pi * integral (cos x)^2 dx from 0 to pi
      f) plot[{2/x,0},{x,1,3}]
         pi * integral (2/x)^2 dx from 1 to 3

21.9  integral pi * (ax)^2 dx from 0 to h

21.10 c) plot[{3sqrt(x),3},{x,0,1}]
         pi * integral x^4/81 dx from 0 to 3
      d) plot[{sqrt(x)},{x,0,5}]
         pi * integral x dx from 0 to 5
      e) plot[{sqrt(4-x^2)},{x,0,pi}]
         pi * integral 4-x^2 dx from 0 to 2

21.11 plot[{sqrt(20^2-x^2),11},{x,0,20},{y,0,20}]
      pi * (4/3*20^3 - integral 20^2-x^2 dx from 11 to 20)

21.12 plot[2x^2,x+1},{x,-0.5,1}]
      pi * integral (x+1)^2-4x^4 dx from -0.5 to 1