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from manimlib.imports import *
class RiemannRectanglesAnimation(GraphScene):
CONFIG = {
"y_max": 5,
"x_max": 6,
"x_min": 0,
"y_min": 0,
"x_axis_width": 5,
"y_axis_height": 5,
"init_dx":0.5,
"graph_origin": ORIGIN+2*DOWN+6*LEFT,
}
def construct(self):
self.setup_axes()
def func(x):
return 0.1*(x)*(x-3)*(x-7)+3
graph1=self.get_graph(func,x_min=0,x_max=6)
kwargs = {
"x_min" : 1.5,
"x_max" : 5.5,
"fill_opacity" : 0.75,
"stroke_width" : 0.25,
"input_sample_type": "right",
}
flat_rectangles1 = self.get_riemann_rectangles(self.get_graph(lambda x : 0),dx=self.init_dx,start_color=invert_color(PURPLE),end_color=invert_color(ORANGE),**kwargs)
riemann_rectangles_list1 = self.get_riemann_rectangles_list(graph1,8,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs)
self.add(graph1)
self.graph_origin = ORIGIN+2*DOWN+1*RIGHT
self.setup_axes()
graph2=self.get_graph(func,x_min=0,x_max=6)
kwargs = {
"x_min" : 1.5,
"x_max" : 5.5,
"fill_opacity" : 0.75,
"stroke_width" : 0.25,
"input_sample_type": "left",
}
flat_rectangles2 = self.get_riemann_rectangles(self.get_graph(lambda x : 0),dx=self.init_dx,start_color=invert_color(PURPLE),end_color=invert_color(ORANGE),**kwargs)
riemann_rectangles_list2 = self.get_riemann_rectangles_list(graph2,8,max_dx=self.init_dx,power_base=2,start_color=PURPLE,end_color=ORANGE,**kwargs)
self.add(graph2)
text1 = TextMobject("Left Riemann sum").move_to(np.array([-3,-2.5,0]))
text2 = TextMobject("Right Riemann sum").move_to(np.array([4,-2.5,0]))
grp1 = VGroup(text1, text2)
text3 = TexMobject(r"n \rightarrow \infty").move_to(np.array([0, -3, 0]))
text4 = TextMobject("Left and Right Riemann sums are equal").move_to(np.array([0, -3, 0]))
text5 = TextMobject("Hence function is Riemann integrable and value of integral equals area covered").move_to(np.array([0, -3, 0])).scale(0.6)
grp2 = VGroup(text1, text2, text3)
# Show Riemann rectangles
self.play(ReplacementTransform(flat_rectangles1,riemann_rectangles_list1[0]), ReplacementTransform(flat_rectangles2, riemann_rectangles_list2[0]))
self.wait()
self.play(ShowCreation(grp1))
for r in range(1,len(riemann_rectangles_list1)-5):
self.transform_between_riemann_rects(riemann_rectangles_list1[r-1],riemann_rectangles_list1[r],replace_mobject_with_target_in_scene = True,)
self.transform_between_riemann_rects(riemann_rectangles_list2[r-1],riemann_rectangles_list2[r],replace_mobject_with_target_in_scene = True,)
self.play(ShowCreation(text3))
for r in range(len(riemann_rectangles_list1)-5,len(riemann_rectangles_list1)):
self.transform_between_riemann_rects(riemann_rectangles_list1[r-1],riemann_rectangles_list1[r],replace_mobject_with_target_in_scene = True,)
self.transform_between_riemann_rects(riemann_rectangles_list2[r-1],riemann_rectangles_list2[r],replace_mobject_with_target_in_scene = True,)
self.wait(2)
self.play(ReplacementTransform(grp2, text4))
self.wait(2)
self.play(ReplacementTransform(text4, text5))
self.wait(4)
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