15.1    a) plot[{3/x^2,0},{x,2,3}]
           integral 3/x^2 dx from 2 to 3
        b) plot[{8-2x^2,0},{x,-2,2}]
           integral 8-2x^2 dx from -2 to 2
        c) plot[{(x-2)^2,x,0},{x,0,4}]
           integral x dx from 0 to 1 + integral (x-2)^2 dx from 1 to 2
        d) plot[{sqrt(x-1),3-x,0},{x,1,3}]
           (integral (sqrt(x-1)) dx from 1 to 2) + integral 3-x dx from 2 to 3
        e) plot[{x^2,2-x},{x,-2,1}]
           integral (2-x)-x^2 dx from -2 to 1
        f) plot[{8-x^2,2x},{x,-4,2}]
           integral 8-x^2-2x dx from -4 to 2
        g) plot[{x,3-x},{x,0,1.5}]
           integral (3-x)-x dx from 0 to 1.5
        h) plot[{x^2/2+2,4},{x,0,2}]
           integral 4-(x^2/2+2) dx from 0 to 2
        i) plot[{x^2,x^(1/3)},{x,0,1}]
           integral x^(1/3)-x^2 dx from 0 to 1

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

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

15.4    integral (1/2 * 3x/5 * 4x/5) dx from 0 to 5

15.5    a) plot[{2x,0},{x,0,3}]
           integral pi * (2x)^2 dx from 0 to 3
        b) plot[{sqrt(x),2},{x,0,4}]
           integral pi * (2^2-(sqrt(x))^2) dx from 0 to 4
        c) plot[{x^2+1,x+1},{x,0,1}]
           integral pi * ((x+1)^2-(1+x^2)^2) dx from 0 to 1
        d) plot[{x^4,1},{x,0,1}]
           integral pi * (1^2-(x^4)^2) dx from 0 to 1
        e) plot[{cos x},{x,0,pi}]
           integral pi * (cos x)^2 dx from 0 to pi

15.6    plot 2x where x=0..5
        integral pi * (2x)^2 dx from 0 to 5

15.7    plot 30-sqrt(30^2-(x)^2) where y=0..10
        pi * integral (30^2-(y-30)^2) dy from 0 to 10