Interactive Integral Plotting

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import sympy; sympy.init_printing(use_unicode=True)

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from sage.symbolic.integration.integral import indefinite_integral

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from sage.symbolic.integration.integral import definite_integral

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@interact

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def _(N=[1,2,3]):

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    var('chi'); Y={1:ln(cos(2*chi))/2,2:exp(chi)+3,3:chi^2/4-0.5}

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    X1={1:0,2:ln(8)/2,3:1}; X2={1:pi/12,2:ln(15)/2,3:2}

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    L=definite_integral((1+diff(Y[N],chi)^2)^0.5,chi,X1[N],X2[N])

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    s1=r'<left><font>$\displaystyle{y=%s; \; FL=%s}$</font></left>'

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    s2=r'<left><font>$\displaystyle{L=%s=%s}$</font></left>'

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    II=indefinite_integral((1+diff(Y[N],chi)^2)^0.5,chi)

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    pretty_print(html(s1%(latex(Y[N]),latex(II))))

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    pretty_print(html(s2%(latex(L),str(L.n()))))

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    M=r'$\mathbb{\alpha}$'; X=[x for x in srange(X1[N],X2[N],.01)]

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    YN=[Y[N](chi=x) for x in X]

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    t=sum([text(M,(x,y),fontsize=12,rgbcolor=Color('#3636ff')) 

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           for (x,y) in list(zip(X,YN))])

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    animate([t+text(M,(x,y),fontsize=14,rgbcolor=Color('#3636ff')) 

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             for (x,y) in list(zip(X,YN))]).show()

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    x=sympy.Symbol('x'); y={1:ln(cos(2*x))/2,2:exp(x)+3,3:x^2/4-.5}

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    L=sympy.Integral(((1+diff(y[N],x)^2)^.5).expand(),(x,X1[N],X2[N]))   

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    print('\nL = '); display(L); print('= '+str(L.n()))

Language: Sage Gap GP HTML Macaulay2 Maxima Octave Python R Singular

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