diff options
Merge pull request #6 from FOSSEE/master
Update fork repo. DONE
Diffstat (limited to 'FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Integral_Properties.py')
| -rw-r--r-- | FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Integral_Properties.py | 77 |
1 files changed, 77 insertions, 0 deletions
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Integral_Properties.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Integral_Properties.py new file mode 100644 index 0000000..97c0e09 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Integral_Properties.py @@ -0,0 +1,77 @@ +from manimlib.imports import *
+from scipy import sin
+class Integral_Properties(GraphScene):
+ CONFIG = {
+ "x_min" : 0,
+ "x_max" : 5,
+ "y_min" : 0,
+ "y_max" : 6,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "axes_color":LIGHT_GRAY,
+ "x_labeled_nums" : list(range(6)),
+ "y_labeled_nums" : list(range(6))
+ }
+ def construct(self):
+ self.setup_axes(animate=False)
+ curve1 = self.get_graph(lambda x : sin(x), x_min=0,x_max=2.5,color=RED)
+ curve2 = self.get_graph(lambda x : x, x_min=0,x_max=2.5,color=DARK_BLUE)
+ curve3 = self.get_graph(lambda x : sin(x) + x, x_min=0,x_max=2.5,color=GREEN)
+ fx = TextMobject(r"$f(x)$").scale(0.5).shift(1*RIGHT+1.8*DOWN)
+ gx = TextMobject(r"$g(x)$").scale(0.5).shift(1*RIGHT)
+ sum = TextMobject(r"$f(x) + g(x)$").scale(0.5).shift(1.3*RIGHT+0.6*UP)
+ area1 = self.get_area(curve1,0,2.5)
+ area2 = self.get_area(curve2,0,2.5)
+ area3 = self.get_area(curve3,0,2.5)
+ area2.set_fill(color=PURPLE)
+ area3.set_fill(color=ORANGE)
+ text1=TextMobject(r"$\int_{0}^{2.5}$ f(x) dx = Area under the curve f(x)",color=BLUE_C).scale(0.7).shift(2.7*RIGHT+3*UP)
+ text2=TextMobject(r"$\int_{0}^{2.5}$ g(x) dx = Area under the curve g(x)",color=PURPLE_B).scale(0.7).shift(2.7*RIGHT+2.4*UP)
+ text3=TextMobject(r"Area under the curve f(x) + g(x) = $\int_{0}^{2.5} (f(x) + g(x)) dx$",color=ORANGE).scale(0.7).shift(2.7*RIGHT+1.8*UP)
+ text4=TextMobject(r"\text{$\int_{0}^{2.5}$ (f(x) + g(x)) dx}",r"\text{ = }",r"\text{ $\int_{0}^{2.5}$ f(x) dx }",r"\text{+}",r"\text{$\int_{0}^{2.5}$ g(x) dx}").scale(0.62).shift(2.7*RIGHT+2.7*UP)
+ text4[0].set_color(ORANGE)
+ text4[2].set_color(BLUE_C)
+ text4[4].set_color(PURPLE_B)
+ self.play(ShowCreation(curve1), ShowCreation(fx))
+ self.wait(1.2)
+ self.play(ShowCreation(curve2),ShowCreation(gx))
+ self.wait(1.2)
+ self.play(ShowCreation(area1))
+ self.play(ShowCreation(text1))
+ self.wait(1.5)
+ self.play(ShowCreation(area2))
+ self.play(ShowCreation(text2))
+ self.wait(1.5)
+ self.play(ShowCreation(curve3),ShowCreation(sum))
+ self.play(ShowCreation(area3))
+ self.play(ShowCreation(text3))
+ self.wait(2)
+ self.play(FadeOut(text1),FadeOut(text2),FadeOut(text3))
+ self.wait(1)
+ self.play(ShowCreation(text4))
+ self.wait(3)
+ self.play(FadeOut(curve1),FadeOut(curve2),FadeOut(area1),FadeOut(area2))
+ self.wait(1.5)
+ self.play(FadeOut(text4),FadeOut(area2),FadeOut(curve2),FadeOut(gx),FadeOut(curve3),FadeOut(sum),FadeOut(area3),ShowCreation(curve1),ShowCreation(fx))
+ self.wait(1.5)
+ self.play(ShowCreation(area1),ShowCreation(text1))
+ self.wait(1.5)
+ curve4 = self.get_graph(lambda x : 2*sin(x), x_min=0,x_max=2.5,color=RED)
+ area4 = self.get_area(curve4,0,2.5)
+ area4.set_fill(color=YELLOW)
+ fx2 = TextMobject(r"$2f(x)$").scale(0.7).shift(1*RIGHT+1.2*DOWN)
+ scalar_mul=TextMobject(r"$\int_{0}^{2.5} ( 2f(x) ) dx$ = 2 $\times$ Area under the curve f(x)",color=YELLOW).scale(0.7).shift(2.7*RIGHT+2.4*UP)
+ self.play(ShowCreation(curve4),ShowCreation(fx2))
+ self.wait(1)
+ self.play(ShowCreation(area4))
+ self.wait(2)
+ self.play(ShowCreation(scalar_mul))
+ self.wait(2)
+ text5=TextMobject(r"\text{$\int_{0}^{2.5}$ (2 f(x)) dx}",r"\text{ = }",r"\text{2 $\int_{0}^{2.5}$ f(x) dx }").scale(0.67).shift(2.7*RIGHT+2.7*UP)
+ text5[0].set_color(YELLOW)
+ text5[2].set_color(BLUE_C)
+ self.play(FadeOut(text1),FadeOut(scalar_mul))
+ self.wait(1)
+ self.play(ShowCreation(text5))
+ self.wait(3)
+
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