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| author | panditsomnath10016git | 2020-05-12 00:19:54 +0530 |
|---|---|---|
| committer | GitHub | 2020-05-12 00:19:54 +0530 |
| commit | 459c8ef6c3efdbb264e0a3eb1687110553571b05 (patch) | |
| tree | 5a7d64f76a20a734f454fe6c6ae84e80dc070c1a /FSF-2020 | |
| parent | 82ee50d6e99250e0a6e3fdda5c261a8da3d8c01f (diff) | |
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Area under a curve as Riemann sum of infinitesimal rectangular regions.
Diffstat (limited to 'FSF-2020')
| -rw-r--r-- | FSF-2020/integrals-of-multivariable-functions/area_under_func.py | 72 |
1 files changed, 72 insertions, 0 deletions
diff --git a/FSF-2020/integrals-of-multivariable-functions/area_under_func.py b/FSF-2020/integrals-of-multivariable-functions/area_under_func.py new file mode 100644 index 0000000..0269d74 --- /dev/null +++ b/FSF-2020/integrals-of-multivariable-functions/area_under_func.py @@ -0,0 +1,72 @@ +from manimlib.imports import * + + +class AreaUnderIntegral(GraphScene): + CONFIG = { + "x_min" : 0, + "x_max" : 5, + "y_min" : 0, + "y_max" : 6, + "Func":lambda x : 1+x**2*np.exp(-.15*x**2) + } + + def construct(self): + X = RIGHT*self.x_axis_width/(self.x_max- self.x_min) + Y = UP*self.y_axis_height/(self.y_max- self.y_min) + + int_area_sym=TextMobject("$$\int_{a}^b f(x)dx$$").shift(2*UP) + area_mean_text = TextMobject(r"means area under the curve of $f(x)$ \\ in the region $a\leq x\leq b$").next_to(int_area_sym,DOWN) + + opening_text=VGroup(*[int_area_sym,area_mean_text]) + self.play(Write(opening_text),run_time=4) + self.wait(2) + self.play(FadeOut(opening_text)) + + self.setup_axes(animate=True) + func= self.get_graph(self.Func, x_min=0,x_max=5) + self.curve=func + + func_text = TextMobject(r"$y = f(x)$").next_to(func,UP) + min_lim = self.get_vertical_line_to_graph(1,func,DashedLine,color=YELLOW) + tick_a=TextMobject(r"$a$").next_to(min_lim,DOWN) + max_lim = self.get_vertical_line_to_graph(4,func,DashedLine,color=YELLOW) + tick_b=TextMobject(r"$b$").next_to(max_lim,DOWN) + + # area = self.get_area(func,1,4) + + self.play(ShowCreation(func), ShowCreation(func_text)) + + self.wait(2) + self.play(ShowCreation(min_lim),Write(tick_a), ShowCreation(max_lim),Write(tick_b),run_time=0.5) + + + approx_text=TextMobject(r"The area can be approximated as \\ sum of small rectangles").next_to(func,4*Y) + self.play(Write(approx_text)) + + rect_list = self.get_riemann_rectangles_list( + self.curve, 5, + max_dx = 0.25, + x_min = 1, + x_max = 4, + ) + flat_graph = self.get_graph(lambda t : 0) + rects = self.get_riemann_rectangles( flat_graph, x_min = 1, x_max = 4, dx = 0.5) + for new_rects in rect_list: + new_rects.set_fill(opacity = 0.8) + rects.align_submobjects(new_rects) + for alt_rect in rects[::2]: + alt_rect.set_fill(opacity = 0) + self.play(Transform( + rects, new_rects, + run_time = 1.5, + lag_ratio = 0.5 + )) + conclude_text=TextMobject(r"Making the rectangles infinitesimally thin \\ we get the real area under the curve.").next_to(func,4*Y) + self.play(Transform(approx_text,conclude_text)) + self.wait(3) + int_area_sym.next_to(self.curve,IN) + self.play(Transform(conclude_text,int_area_sym)) + + # self.play(ShowCreation(area)) + self.wait(3) + |