23.1 1*30+1*56+1*25+1*38+1*33+1*28+1*15+1*5+1*15+1*0
     1*0+1*30+1*56+1*25+1*38+1*33+1*28+1*15+1*5+1*15


23.2 a) integrate (3x) dx from 0 to 3
        Plot[{3x,Piecewise[{{0, 0<=x<=1}, {3, 2>x>1}, {6, 3>x>2}}]},{x, 0, 3}]
        Plot[{3x,Piecewise[{{3, 0<=x<=1}, {6, 2>x>1}, {9, 3>x>2}}]}, {x, 0, 3}]
        Plot[{3x,Piecewise[{{1.5, 0<=x<=1}, {4.5, 2>x>1}, {7.5, 3>x>2}}]}, {x, 0, 3}]
        sum 1*3*(n*1) where n =0..2
        sum 1*3*(n*1) where n =1..3
        sum 1*3*(n*1-0.5) where n =1..3
        sum 3/10*3*(n*3/10) where n =0..9
        sum 3/10*3*(n*3/10) where n =1..10
        sum 3/10*3*(n*3/10-1.5/10) where n =1..10
     c) integrate (4x-x^2) dx from 1 to 4
        Plot[{4x-x^2,Piecewise[{{4*1.0-1.0^2, 1.5>x>1}, {4*1.5-1.5^2, 2>x>1.5}, {4*2.0-2.0^2, 2.5>x>2}, {4*2.5-2.5^2, 3>x>2.5}, {4*3.0-3.0^2, 3.5>x>3}, {4*3.5-3.5^2, 4>x>3.5}}]}, {x, 1, 4}]
        Plot[{4x-x^2,Piecewise[{{4*1.5-1.5^2, 1.5>x>1}, {4*2.0-2.0^2, 2>x>1.5}, {4*2.5-2.5^2, 2.5>x>2}, {4*3.0-3.0^2, 3>x>2.5}, {4*3.5-3.5^2, 3.5>x>3}, {4*4.0-4.0^2, 4>x>3.5}}]}, {x, 1, 4}]
        Plot[{4x-x^2,Piecewise[{{4*1.25-1.25^2, 1.5>x>1}, {4*1.75-1.75^2, 2>x>1.5}, {4*2.25-2.25^2, 2.5>x>2}, {4*2.75-2.75^2, 3>x>2.5}, {4*3.25-3.25^2, 3.5>x>3}, {4*3.75-3.75^2, 4>x>3.5}}]}, {x, 1, 4}]
        sum 1/2*(4*(1+n*1/2)-(1+n*1/2)^2)) where n =0..5
        sum 1/2*(4*(1+n*1/2)-(1+n*1/2)^2) where n =1..6
        sum 1/2*(4*(1+n*1/2-1/4)-(1+n*1/2-1/4)^2) where n =1..6
        sum 3/10*(4*(1+n*3/10)-(1+n*3/10)^2) where n =0..9
        sum 3/10*(4*(1+n*3/10)-(1+n*3/10)^2) where n =1..10
        sum 3/10*(4*(1+n*3/10-1.5/10)-(1+n*3/10-1.5/10)^2) where n =1..10
     d) integrate sqrt(x) dx from 1 to 4
        Plot[{sqrt(x), Piecewise[{{sqrt(1), 2.0>x>1.00}, {sqrt(2), 3.0>x>2.00}, {sqrt(3), 4.0>x>3.00}}]}, {x, 1, 4}]
        Plot[{sqrt(x), Piecewise[{{sqrt(2), 2.0>x>1.00}, {sqrt(3), 3.0>x>2.00}, {sqrt(4), 4.0>x>3.00}}]}, {x, 1, 4}]
        Plot[{sqrt(x), Piecewise[{{sqrt(1.5), 2.0>x>1.00}, {sqrt(2.5), 3.0>x>2.00}, {sqrt(3.5), 4.0>x>3.00}}]}, {x, 1, 4}]
        sum 1*sqrt(1+n*1) where n =0..2
        sum 1*sqrt(1+n*1) where n =1..3
        sum 1*sqrt(1+n*1-0.5) where n =1..3
        sum 1/4*sqrt(1+n*1/4) where n =0..11
        sum 1/4*sqrt(1+n*1/4) where n =1..12
        sum 1/4*sqrt(1+n*1/4-1/8) where n =1..12

26.1 a) plot x^2, 2-x
        integrate 2-x-x^2 dx from -2 to 1
     b) plot sqrt(4-x^2) where x from -2 to 2
        integrate sqrt(4-x^2) dx from -2 to 2
     c) plot x^2,x^3 where x from -0.25 to 1.25
        integrate x^2-x^3 dx from 0 to 1
     d) plot x^2/4,x,1 where x from -2 to 1
        integrate 1-x^2/4 dx from -2 to 0 + integrate 1-x dx from 0 to 1
     f) plot x^3/3-x, x/3
        integrate |x/3-(x^3/3-x)| dx from -2 to 2

23.3 a) integrate (x/2+3) dx from -2 to 4
     b) integrate sqrt(9-x^2) dx from -3 to 3
     c) integrate 1-|x| dx from -1 to 1
     d) integrate (1+sqrt(1-x^2)) dx from -1 to 1
  
23.4 a) integrate (1-x^2) dx from 0 to 1
        1/6*((1-0^2)+2*((1-(1/3)^2)+(1-(2/3)^2))+(1-1^2))
     b) integrate (1-sqrt(x)) dx from 1 to 4
        1/4*(1+sqrt(1)+2*(1+sqrt(1.5)+1+sqrt(2)+1+sqrt(2.5)+1+sqrt(3)+1+sqrt(3.5))+1+sqrt(4))
     c) integrate sqrt(1+x) dx from 3 to 8
        1/2*(sqrt(1+3)+2*(sqrt(1+4)+sqrt(1+5)+sqrt(1+6)+sqrt(1+7))+sqrt(1+8))

23.6 a) integrate (1+x^3) dx from 0 to 2
        1/3*(1+(0)^3+4*1+(1)^3+1+(2)^3)
     b) integrate x^(1/3) dx from 0 to 8
        2/3*((0)^(1/3)+4*(2)^(1/3)+2*(4)^(1/3)+4*(6)^(1/3)+1*(8)^(1/3))

23.7 100*integrate (4+sqrt(1+8x-2x^2)) dx from 0 to 4
     100/4*(4+sqrt(1+8(0)-2(0)^2)+2*(sum(4+sqrt(1+8(n*0.5)-2(n*0.5)^2)),n=1..7)+4+sqrt(1+8(4)-2(4)^2))
     100/6*(4+sqrt(1+8(0)-2(0)^2)+4*(sum(4+sqrt(1+8(n+0.5)-2(n+0.5)^2)),n=0..3)+2*(sum(4+sqrt(1+8(n)-2(n)^2)),n=1..3)+4+sqrt(1+8(4)-2(4)^2))