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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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