a=0

a =

     0

b=pi/2

b =

    1.5708

N=4

N =

     4

x=linspace(a,b,N+1)

x =

         0    0.3927    0.7854    1.1781    1.5708

f=sin(x)

f =

         0    0.3827    0.7071    0.9239    1.0000

deltax(b-a)/N
??? Undefined command/function 'deltax'.

deltax=(b-a)/N

deltax =

    0.3927

left=sum(f(1:N))*deltax

left =

    0.7908

right=sum(f(2:N+1))*deltax

right =

    1.1835

trap=(left+right)/2

trap =

    0.9871

xmid=x+deltax/2

xmid =

    0.1963    0.5890    0.9817    1.3744    1.7671

fmid=sin(xmid)

fmid =

    0.1951    0.5556    0.8315    0.9808    0.9808

mid=sum(fmid(1:N))*deltax

mid =

    1.0065

simpson=(2*mid+trap)/3

simpson =

    1.0000

format long
left=sum(f(1:N))*deltax

left =

   0.79076626012341

right=sum(f(2:N+1))*deltax

right =

   1.18346534182214

trap=(left+right)/2

trap =

   0.98711580097278

mid=sum(fmid(1:N))*deltax

mid =

   1.00645454279956

simpson=(2*mid+trap)/3

simpson =

   1.00000829552397

lefterror=left-1

lefterror =

  -0.20923373987659

righterror=right-1

righterror =

   0.18346534182214

miderror=mid-1

miderror =

   0.00645454279956

traperror=trap-1

traperror =

  -0.01288419902722

simpsonerror=simpson-1

simpsonerror =

    8.295523967527529e-006

N=8

N =

     8

x=linspace(a,b,N+1)

x =

  Columns 1 through 5 

                  0   0.19634954084936   0.39269908169872   0.58904862254809   0.78539816339745

  Columns 6 through 9 

   0.98174770424681   1.17809724509617   1.37444678594553   1.57079632679490

f=sin(x)

f =

  Columns 1 through 5 

                  0   0.19509032201613   0.38268343236509   0.55557023301960   0.70710678118655

  Columns 6 through 9 

   0.83146961230255   0.92387953251129   0.98078528040323   1.00000000000000

deltax(b-a)/N
??? Subscript indices must either be real positive integers or logicals.

deltax=(b-a)/N

deltax =

   0.19634954084936

xmid=x+deltax/2

xmid =

  Columns 1 through 5 

   0.09817477042468   0.29452431127404   0.49087385212341   0.68722339297277   0.88357293382213

  Columns 6 through 9 

   1.07992247467149   1.27627201552085   1.47262155637022   1.66897109721958

fmid=sin(xmid)

fmid =

  Columns 1 through 5 

   0.09801714032956   0.29028467725446   0.47139673682600   0.63439328416365   0.77301045336274

  Columns 6 through 9 

   0.88192126434835   0.95694033573221   0.99518472667220   0.99518472667220

left=sum(f(1:N))*deltax

left =

   0.89861040146149

right=sum(f(2:N+1))*deltax

right =

   1.09495994231085

mid=sum(fmid(1:N))*deltax

mid =

   1.00160818908398

trap=(left+right)/2

trap =

   0.99678517188617

simpsonerror=simpson-1

simpsonerror =

    8.295523967527529e-006

simpson=(2*mid+trap)/3

simpson =

   1.00000051668471

lefterror=left-1

lefterror =

  -0.10138959853851

righterror=right-1

righterror =

   0.09495994231085

traperror=trap-1

traperror =

  -0.00321482811383

miderror=mid-1

miderror =

   0.00160818908397

simpsonerror=simpson-1

simpsonerror =

    5.166847065751767e-007

mid=sum(fmid(1:N))*deltax

mid =

   1.00160818908398

miderror=mid-1

miderror =

   0.00160818908397

diary off