Interactive: Definite Integral

# Definite Integral # Lauri Ruotsalainen, 2010 @interact def definite_integral( f = input_box(default = 3*x), g = input_box(default = x^2), interval = input_box(default=(0,3), label="Interval"), x_range = input_box(default=(0,3), label = "Plotting range (x)"), selection = selector(["f", "g", "f and g", "f - g"], label="Select") ): f(x) = f; g(x) = g f_plot = Graphics(); g_plot = Graphics(); h_plot = Graphics(); text = "" # Plot function f. if selection != "g": f_plot = plot(f(x), x, x_range, color="blue", thickness=1.5) # Color and calculate the area between f and the horizontal axis. if selection == "f" or selection == "f and g": f_plot += plot(f(x), x, interval, color="blue", fill=True, fillcolor="blue", fillalpha=0.15) text += "$\int_%s^%s(\color{Blue}{f(x)})\,dx=\int_%s^%s(%s)\,dx=%s$" % ( interval[0], interval[1], interval[0], interval[1], latex(f(x)), f(x).nintegrate(x, interval[0], interval[1])[0] ) # Plot function g. Also color and calculate the area between g and the horizontal axis. if selection == "g" or selection == "f and g": g_plot = plot(g(x), x, x_range, color="green", thickness=1.5) g_plot += plot(g(x), x, interval, color="green", fill=True, fillcolor="yellow", fillalpha=0.5) text += "\n$\int_%s^%s(\color{Green}{g(x)})\,dx=\int_%s^%s(%s)\,dx=%s$" % ( interval[0], interval[1], interval[0], interval[1], latex(g(x)), g(x).nintegrate(x, interval[0], interval[1])[0] ) # Plot function f-g. Also color and calculate the area between f-g and the horizontal axis. if selection == "f - g": g_plot = plot(g(x), x, x_range, color="green", thickness=1.5) g_plot += plot(g(x), x, interval, color="green", fill=f(x), fillcolor="red", fillalpha=0.15) h_plot = plot(f(x)-g(x), x, interval, color="red", thickness=1.5, fill=True, fillcolor="red", fillalpha=0.15) text = "$\int_%s^%s(\color{Red}{f(x)-g(x)})\,dx=\int_%s^%s(%s)\,dx=%s$" % ( interval[0], interval[1], interval[0], interval[1], latex(f(x)-g(x)), (f(x)-g(x)).nintegrate(x, interval[0], interval[1])[0] ) show(f_plot + g_plot + h_plot, gridlines=True) html(text)