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author | Somnath Pandit | 2020-05-26 14:38:07 +0530 |
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committer | Somnath Pandit | 2020-05-26 14:38:07 +0530 |
commit | a92ab419ce219a9bab4bbe03ea0f8be004e640ea (patch) | |
tree | 7c698a5b6b21e0174635a69ae609465a1bc8cac1 /FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/non_rect_region.py | |
parent | f26d34f6f654c5070fd62b92c8bb59f9e5b00762 (diff) | |
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renamed files
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/non_rect_region.py')
-rw-r--r-- | FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/non_rect_region.py | 154 |
1 files changed, 0 insertions, 154 deletions
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/non_rect_region.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/non_rect_region.py deleted file mode 100644 index 793a000..0000000 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/non_rect_region.py +++ /dev/null @@ -1,154 +0,0 @@ -from manimlib.imports import * - -class AreaUnderCurve(GraphScene): - CONFIG = { - "x_min" : -1, - "x_max" : 8, - "y_min" : -1, - "y_max" : 5, - "y_axis_label": "$y$", - "x_tick_frequency" : 1, - "y_tick_frequency" : 1, - "x_labeled_nums": list(np.arange(-1, 9)), - "y_labeled_nums": list(np.arange(-1, 6)), - "y_axis_height":5.5, - "graph_origin": ORIGIN+4*LEFT+2.5*DOWN, - } - - 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) - - sofar_text=TextMobject(r"So far we have integrated over \\ rectangular regions") - self.play(Write(sofar_text)) - self.play(sofar_text.to_edge,UP) - - self.setup_axes(animate=False) - - rect= self.get_graph( - lambda x : 3, - x_min = 0, - x_max = 5, - color = GREEN) - - rect_region = self.get_riemann_rectangles( - rect, - x_min = 0, - x_max = 5, - dx =.01, - start_color = GREEN, - end_color = GREEN, - fill_opacity = 0.75, - stroke_width = 0, - ) - - self.play(ShowCreation(rect_region)) - self.wait(.5) - - rect_int=TextMobject(r"Here the integration limits are set as").to_edge(UP) - rect_lim=TextMobject(r"$$\int_{x=0}^{5}\int_{y=0}^{3}$$").next_to(rect_int,DOWN) - const_text=TextMobject(r"$\longleftarrow $ \textsf the limits are\\ constant values").next_to(rect_lim,RIGHT) - - self.play(ReplacementTransform(sofar_text,rect_int)) - self.wait(1.5) - self.play(FadeIn(rect_lim)) - self.wait(2) - self.play(Write(const_text)) - self.wait(2) - self.play(FadeOut(rect_int), FadeOut(rect_lim),FadeOut(const_text)) - - - non_rect_text=TextMobject(r"Now we see how to integrate over \\ non-rectangular regions") - non_rect_text.to_edge(UP) - self.play(Write(non_rect_text)) - self.wait(1.5) - self.play(FadeOut(rect_region)) - - c1= self.get_graph( - lambda x : x**2/4, - x_min = 0, - x_max = 4, - color = RED) - - c1_region = self.get_riemann_rectangles( - c1, - x_min = 0, - x_max = 4, - dx =.01, - start_color = BLUE, - end_color = BLUE, - fill_opacity = 0.75, - stroke_width = 0, - ) - self.add(c1,c1_region) - # self.wait(2) - - c2= self.get_graph( - lambda x :12-2*x, - x_min = 4, - x_max = 6, - color = RED) - - c2_region = self.get_riemann_rectangles( - c2, - x_min = 4, - x_max = 6, - dx =.01, - start_color = BLUE, - end_color = BLUE, - fill_opacity = .75, - stroke_width = 0, - ) - self.add(c2_region,c2) - self.wait(1.5) - c=VGroup(*[c1,c2]) - - no_func_text=TextMobject(r"The whole region can't be expressed as\\ bounded by a single $f(x)$").next_to(c2,UP,buff=LARGE_BUFF) - - self.play(ReplacementTransform(non_rect_text,no_func_text)) - self.wait(1) - self.play(Indicate(c)) - self.wait(2) - - div_region_text=TextMobject(r"So the region is divided into two").next_to(c2,UP,buff=MED_LARGE_BUFF) - self.play(ReplacementTransform(no_func_text,div_region_text)) - - c2.set_color(YELLOW) - self.play(c2_region.set_color,YELLOW) - c1_text=TextMobject("$\dfrac{x^2}{4}$").next_to(c1,IN) - c2_text=TextMobject("$12-2x$").next_to(c2,IN+2*X) - c_text=VGroup(*[c1_text,c2_text]) - - self.play(FadeIn(c_text)) - self.wait(.4) - self.play(Indicate(c1),Indicate(c1_text)) - self.play(Indicate(c2),Indicate(c2_text)) - - easy_text=TextMobject(r"Now the limis can be set easily").next_to(c2,UP,buff=.5) - self.play(ReplacementTransform(div_region_text,easy_text)) - - c1_int=TextMobject(r"$$\int_{x=0}^{4}\int_{y=0}^{\dfrac{x^2}{4}}$$").next_to(c1,IN).shift(.5*(-X+1.3*Y)) - c2_int=TextMobject(r"$$\int_{x=4}^{6}\int_{y=0}^{12-2x}$$").next_to(c2,IN+X) - - self.play(ReplacementTransform(c1_text,c1_int),ReplacementTransform(c2_text,c2_int)) - self.wait(2) - - total_int=TextMobject(r"The total integraton= ").to_edge(UP) - plus=TextMobject("$$+$$").move_to(self.graph_origin+4*X+4.8*Y) - self.play(ReplacementTransform(easy_text,total_int)) - self.play(c2_region.set_color,BLUE) - self.play(c1_int.next_to,c1,.1*UP, c2_int.next_to,plus,RIGHT, FadeIn(plus)) - - region=VGroup(*[c1_region,c2_region]) - region.set_color(GREEN) - self.play(ShowCreation(region)) - self.wait(3) - - - -#uploaded by Somnath Pandit.FSF2020_Double_Integral - - - - - |