added curvy_region

3 files changed, 107 insertions, 0 deletions

diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/README.md b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/README.md
index 23e2423..0cd6968 100644
--- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/README.md
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/README.md
@@ -29,3 +29,8 @@ FSF2020--Somnath Pandit
 

 **file3_iteration_methods**

 ![file3_iteration_methods](https://github.com/panditsomnath10016git/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/file3_iteration_methods.gif)

+

+**file4_curvy_limits**

+![file4_curvy_limits](https://github.com/panditsomnath10016git/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/file4_curvy_region.gif)

+

+

diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/file4_curvy_region.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/file4_curvy_region.gif
new file mode 100644
index 0000000..b0620e5
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/file4_curvy_region.gif
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/file4_curvy_region.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/file4_curvy_region.py
new file mode 100644
index 0000000..46134a7
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's-theorem/file4_curvy_region.py
@@ -0,0 +1,102 @@
+from manimlib.imports import *
+
+class CurvyRegion(GraphScene):
+    CONFIG = {
+    "x_min": 0,
+    "x_max": 8,
+    "y_min": 0,
+    "y_max": 6,
+    "graph_origin": ORIGIN+4.5*LEFT+3*DOWN,
+    "x_labeled_nums": np.arange(0, 9,2),
+    "y_labeled_nums": np.arange(0, 7,2),
+    "x_axis_width": 6,
+    "y_axis_height": 6,
+    }
+	
+    def construct(self):
+        XD = self.x_axis_width/(self.x_max- self.x_min)
+        YD = self.y_axis_height/(self.y_max- self.y_min)
+        self.X=XD*RIGHT ;self.Y=YD*UP
+                
+        sin_curve_points=[self.graph_origin+(2+.5*np.sin(2*y),y,0) 
+            for y in np.arange(1,5,.005)]
+        
+        cos_curve_points=[self.graph_origin+(
+            5+.5*np.cos(2*y),y,0)  
+            for y in np.arange(1,5,.005)]
+        cos_curve_points.reverse()
+        
+        region=Polygon(
+            *sin_curve_points+cos_curve_points,
+            color=YELLOW,
+            stroke_width=1,  
+            fill_color=BLUE_E,
+            fill_opacity=.75
+        )
+        
+        line=Line((1,0,0),(1,6,0),color=RED)
+        line.move_to(self.graph_origin+2.5*self.X,DOWN)
+        self.line=line
+        self.setup_axes(animate = False)
+        
+        self.add(region)
+        self.wait()
+        self.first_y_int_scene()
+        self.try_x_first_scene()
+        
+        
+    def first_y_int_scene(self):
+        talk=TextMobject(r"For doing the $y$ integration\\ first we need to set\\ proper $y$ limts").to_corner(UR,buff=LARGE_BUFF)
+        problem=TextMobject(r"But here we get\\ more than two $y$ values\\ for a single $x$ value" ).to_corner(UR,buff=LARGE_BUFF)
+        int_y=TextMobject("$$\\int_?^? dy$$").next_to(problem,DOWN,buff=.5)
+        
+        self.play(Write(talk))
+        self.play(FadeIn(self.line))
+        self.wait(2)
+        self.play(ReplacementTransform(talk,problem))
+        self.play(
+            ApplyMethod(self.line.shift,3.7*self.X),
+            run_time=4
+        )
+        self.wait()
+        self.play(Write(int_y))
+        self.wait(3)
+        self.play(FadeOut(VGroup(problem,int_y,self.line)))
+
+    def try_x_first_scene(self):
+        try_text=TextMobject(r"But if we try to integrate\\ along $x$ first ...." ).to_corner(UR,buff=LARGE_BUFF)
+        good_limits=TextMobject(r"For one $y$ value we get\\ only \textbf{two} $x$ values $\dots$").to_corner(UR,buff=LARGE_BUFF)
+        limit_values= TextMobject(r"one Lower limit\\ one Upper limit ").next_to(good_limits,DOWN,buff=.5)
+        int_x=TextMobject("$$\\int_{f(y)}^{g(y)} dx$$").next_to(limit_values,DOWN)
+        
+        self.setup_line()
+        self.play(Write(try_text))
+        self.play(FadeIn(self.line))
+        self.wait()
+        self.play(ReplacementTransform(try_text,good_limits))
+        self.wait()
+        self.play(
+            ApplyMethod(self.line.shift,3*self.Y),
+            run_time=4
+        )
+        self.play(Write(limit_values))
+        self.wait()
+        self.show_functions()
+        self.play(Write(int_x))
+        self.wait(3)
+        
+    def setup_line(self):
+        line=self.line.rotate(PI/2)
+        line.move_to(self.graph_origin+.5*self.X+1.5*self.Y,LEFT)
+        self.line=line
+        
+    def show_functions(self):
+        fy=TextMobject("$$f(y)$$")
+        gy=TextMobject("$$g(y)$$")
+        fy.move_to(self.graph_origin+2*self.X+3.3*self.Y)
+        gy.move_to(self.graph_origin+7*self.X+2*self.Y)
+        self.play(FadeIn(VGroup(fy,gy)))
+        
+        
+  #uploaded by Somnath Pandit.FSF2020_Fubini's_Theorem   
+