1 files changed, 73 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file1_area_under_func.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file1_area_under_func.py
new file mode 100644
index 0000000..773840c
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file1_area_under_func.py
@@ -0,0 +1,73 @@
+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)
+        
+#uploaded by Somnath Pandit.FSF2020_Double_Integral