f(x)=1/x^2
plot(f(x), (x, -2, 1), ymax=5, fill=True)
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integral(f(x), x, -2, 1)
Traceback (click to the left of this block for traceback) ... ValueError: Integral is divergent. Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "_sage_input_3.py", line 10, in <module>
exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("aW50ZWdyYWwoZih4KSwgeCwgLTIsIDEp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
File "", line 1, in <module>
File "/tmp/tmpU5BXF9/___code___.py", line 3, in <module>
exec compile(u'integral(f(x), x, -_sage_const_2 , _sage_const_1 )
File "", line 1, in <module>
File "/usr/local/sage-5.12/local/lib/python2.7/site-packages/sage/misc/functional.py", line 748, in integral
return x.integral(*args, **kwds)
File "expression.pyx", line 9759, in sage.symbolic.expression.Expression.integral (sage/symbolic/expression.cpp:40828)
File "/usr/local/sage-5.12/local/lib/python2.7/site-packages/sage/symbolic/integration/integral.py", line 692, in integrate
return definite_integral(expression, v, a, b)
File "function.pyx", line 789, in sage.symbolic.function.BuiltinFunction.__call__ (sage/symbolic/function.cpp:7825)
File "function.pyx", line 430, in sage.symbolic.function.Function.__call__ (sage/symbolic/function.cpp:5161)
File "/usr/local/sage-5.12/local/lib/python2.7/site-packages/sage/symbolic/integration/integral.py", line 173, in _eval_
return integrator(*args)
File "/usr/local/sage-5.12/local/lib/python2.7/site-packages/sage/symbolic/integration/external.py", line 21, in maxima_integrator
result = maxima.sr_integral(expression, v, a, b)
File "/usr/local/sage-5.12/local/lib/python2.7/site-packages/sage/interfaces/maxima_lib.py", line 740, in sr_integral
raise ValueError, "Integral is divergent."
ValueError: Integral is divergent.
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예.
f(x)=1/sqrt(4-x^2)
plot(f(x), (x, 0, 2), fill=True)
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integral(f(x), x, 0, 2)
1/2*pi 1/2*pi |
예제 8.
var('x, y')
F(x, y)=x^(2/3)+y^(2/3)-1
implicit_plot(F(x, y)==0, (x, 0, 1), (y, 0, 1)) # 제 1사분면만 그림
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Fx=diff(F(x, y), x)
Fy=diff(F(x, y), y)
dydx=-Fx/Fy
print dydx # 도함수
-y^(1/3)/x^(1/3) -y^(1/3)/x^(1/3) |
1+dydx^2
y^(2/3)/x^(2/3) + 1 y^(2/3)/x^(2/3) + 1 |
integral(1/x^(1/3), x, 0, 1)
3/2 3/2 |
예제 10.
f(x)=1/(x-1)^(2/3)
plot(f(x), (x, 0, 3), fill=True, ymax=5)
verbose 0 (2395: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 66 points. verbose 0 (2395: plot.py, generate_plot_points) Last error message: 'negative number to a fractional power not real' verbose 0 (2395: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 66 points. verbose 0 (2395: plot.py, generate_plot_points) Last error message: 'negative number to a fractional power not real' |
integral(f(x), x, 0, 3)
3*2^(1/3) - 3*(-1)^(1/3) 3*2^(1/3) - 3*(-1)^(1/3) |
(3*2^(1/3)).n(digits=5)
3.7798 3.7798 |
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