1638.sagews

print "Mark Sakurada"
print "Lab 1 Calc II"

Mark Sakurada Lab 1 Calc II

x=var('x')
n=var('n')
n=8
f=sqrt(x)
p1=plot(f,(x,0,4))
for i in range(0,n,1):p1+=polygon([(i/2,0), (i/2+4/n,0), (i/2+4/n,f(i/2+4/n)), (i/2,f(i/2+4/n))],  rgbcolor=(1/8,3/4,1/2))
aa=var('aa')
xi=var('xi')
aa=0
xi=0
for j in range (0,8,1):xi=xi+4/n; aa=aa+f(xi)*4/n
print "aa= %s" %N(aa,digits=4)
ae=integral(f(x), x, 0, 4)
print "ae= %s" %N(ae, digits=4)
print " %s percent" %N((aa-ae)/ae *100, digits=2)
p1

aa= 5.765 ae= 5.333 8.1 percent

x=var('x')
n=var('n')
b=var('b')
n=8
b=pi
f(x)=sin(x)
p2=plot(f,(x,0,pi))
for i in range(0,n*pi-.5,pi):p2+=polygon([(i/n,0), (i/n+b/n,0), (i/n+b/n,f(i/n+b/n)), (i/n,f(i/n+b/n))],  rgbcolor=(1/8,3/4,1/2))
aa=var('aa')
xi=var('xi')
aa=0
xi=0
for j in range (0,n*pi,pi):xi=xi+b/n; aa=aa+f(xi)*b/n
print "aa= %s" %N(aa,digits=4)
ae=integral(f(x), x, 0, b)
print "ae= %s" %N(ae, digits=4)
print " %s percent" %N((aa-ae)/ae *100, digits=4)
p2

aa= 1.824 ae= 2.000 -8.803 percent

x=var('x')
n=var('n')
b=var('b')
n=64
b=pi
f(x)=sin(x)
p2=plot(f,(x,0,pi))
for i in range(0,n*pi-.5,pi):p2+=polygon([(i/n,0), (i/n+b/n,0), (i/n+b/n,f(i/n+b/n)), (i/n,f(i/n+b/n))],  rgbcolor=(1/8,3/4,1/2))
aa=var('aa')
xi=var('xi')
aa=0
xi=0
for j in range (0,n*pi,pi):xi=xi+b/n; aa=aa+f(xi)*b/n
print "aa= %s" %N(aa,digits=4)
ae=integral(f(x), x, 0, b)
print "ae= %s" %N(ae, digits=4)
print " %s percent" %N((aa-ae)/ae *100, digits=4)
p2

aa= 1.985 ae= 2.000 -0.7419 percent

x=var('x')
n=var('n')
b=var('b')
b=2
n=8
f=2/(x^2+(4*x)+8)
p1=plot(f,(x,-5,1))
for i in range(-8,0,1):p1+=polygon([(i/4,0), (i/4+b/n,0), (i/4+b/n,f(i/4+b/n)), (i/4,f(i/4+b/n))],  rgbcolor=(1/8,3/4,1/2))
aa=var('aa')
xi=var('xi')
aa=0
xi=-2
for j in range (-8,0,1):xi=j/4+2/n; aa=aa+f(xi)*2/n
print "aa= %s" %N(aa,digits=4)
ae=integral(f(x), x, -2, 0)
print "ae= %s" %N(ae, digits=4)
print " %s percent" %N((aa-ae)/ae *100, digits=4)
p1

aa= 0.7535 ae= 0.7854 -4.062 percent