#FUNCIÓN PRINCIPAL t=var('t') h1(t)=(11*((t)^2)/4)+3;h2(t)=(-2*(t)^2)+4 f=piecewise([[(-pi,0),h1(t)],[(0,pi),h2(t)]]) uta=plot(f(t),(t,-pi,pi)) uta w1(t)=sin(t) w2(t)=sin(2*t) w3(t)=sin(3*t)
s=integral(w1(t),t,0,pi) s s1=integral(w2(t),t,0,pi) s1 s2=integral(w3(t),t,0,pi) s2 k1=integral(w1(t)*h1(t),t,-pi,0)+integral(w1(t)*h2(t),t,0,pi) k2=integral(w2(t)*h1(t),t,-pi,0)+integral(w2(t)*h2(t),t,0,pi) k3=integral(w3(t)*h1(t),t,-pi,0)+integral(w3(t)*h2(t),t,0,pi)
pi
0
0
nor=integral((w1(t))^2,t,-pi,pi)
nor
pi
nor1=integral((w2(t))^2,t,-pi,pi)
nor1
pi
theta1(t)=k1/nor*w1(t) theta2(t)=k1/nor*w1(t)+k2/nor*w2(t) theta3(t)=k1/nor*w1(t)+k2/nor*w2(t)+k3/nor*w3(t)
uta1=plot(theta1(t),(t,-pi,pi),color='yellow') uta2=plot(theta2(t),(t,-pi,pi),color='green') uta3=plot(theta3(t),(t,-pi,pi),color='purple')
mett=uta+uta1+uta2+uta3
#3(a).LA FUNCION PRINCIPAL ES LA AZUL #la mas cercana es w1 porque la funcion principal tiene valor de 29.74 al integrarla y al integrar las demas el mayor numero fue el de w1 y ya que la diferencia entre la principal y esta ultima va a ser menor esto quiere decir que es la mas cercana mett.show()
w1(t)=1 w2(t)=cos(t) w3(t)=cos(3*t) w4(t)=cos(5*t) s3=integral(w1(t),t,0,pi) s3 s4=integral(w2(t),t,0,pi) s4 s5=integral(w3(t),t,0,pi) s5 k1=integral(w1(t)*h1(t),t,-pi,0)+integral(w1(t)*h2(t),t,0,pi) k2=integral(w2(t)*h1(t),t,-pi,0)+integral(w2(t)*h2(t),t,0,pi) k3=integral(w3(t)*h1(t),t,-pi,0)+integral(w3(t)*h2(t),t,0,pi) k4=integral(w4(t)*h1(t),t,-pi,0)+integral(w4(t)*h2(t),t,0,pi) nor=integral((w1(t))^2,t,-pi,pi) nor theta1(t)=k1/nor*w1(t) theta2(t)=k1/nor*w1(t)+k2/nor*w2(t) theta3(t)=k1/nor*w1(t)+k2/nor*w2(t)+k3/nor*w3(t) theta4(t)=k1/nor*w1(t)+k2/nor*w2(t)+k3/nor*w3(t)+k4/nor*w4(t) uta1=plot(theta1(t),(t,-pi,pi),color='yellow') uta2=plot(theta2(t),(t,-pi,pi),color='green') uta3=plot(theta3(t),(t,-pi,pi),color='purple') uta4=plot(theta4(t),(t,-pi,pi),color='red') mett=uta+uta1+uta2+uta3+uta4 mett.show() #3(b).LA FUNCION PRINCIPAL ES LA AZUL #la mas cercana es w4
pi
0
0
2*pi
w1(t)=1 w2(t)=sin(t) w3(t)=sin(2*t) w4(t)=sin(3*t) w5(t)=cos(t) w6(t)=cos(3*t) w7(t)=cos(5*t) k1=integral(w1(t)*h1(t),t,-pi,0)+integral(w1(t)*h2(t),t,0,pi) k2=integral(w2(t)*h1(t),t,-pi,0)+integral(w2(t)*h2(t),t,0,pi) k3=integral(w3(t)*h1(t),t,-pi,0)+integral(w3(t)*h2(t),t,0,pi) k4=integral(w4(t)*h1(t),t,-pi,0)+integral(w4(t)*h2(t),t,0,pi) k5=integral(w5(t)*h1(t),t,-pi,0)+integral(w5(t)*h2(t),t,0,pi) k6=integral(w6(t)*h1(t),t,-pi,0)+integral(w6(t)*h2(t),t,0,pi) k7=integral(w7(t)*h1(t),t,-pi,0)+integral(w7(t)*h2(t),t,0,pi) nor=integral((w1(t))^2,t,-pi,pi) nor theta1(t)=k1/nor*w1(t) theta2(t)=k1/nor*w1(t)+k2/nor*w2(t) theta3(t)=k1/nor*w1(t)+k2/nor*w2(t)+k3/nor*w3(t) theta4(t)=k1/nor*w1(t)+k2/nor*w2(t)+k3/nor*w3(t)+k4/nor*w4(t) theta5(t)=k1/nor*w1(t)+k2/nor*w2(t)+k3/nor*w3(t)+k4/nor*w4(t)+k5/nor*w5(t) theta6(t)=k1/nor*w1(t)+k2/nor*w2(t)+k3/nor*w3(t)+k4/nor*w4(t)+k5/nor*w5(t)+k6/nor*w6(t) theta7(t)=k1/nor*w1(t)+k2/nor*w2(t)+k3/nor*w3(t)+k4/nor*w4(t)+k5/nor*w5(t)+k6/nor*w6(t)+k7/nor*w7(t) uta1=plot(theta1(t),(t,-pi,pi),color='yellow') uta2=plot(theta2(t),(t,-pi,pi),color='green') uta3=plot(theta3(t),(t,-pi,pi),color='purple') uta4=plot(theta4(t),(t,-pi,pi),color='red') uta5=plot(theta4(t),(t,-pi,pi),color='orange') uta6=plot(theta4(t),(t,-pi,pi),color='brown') uta7=plot(theta4(t),(t,-pi,pi),color='gold') mett=uta+uta1+uta2+uta3+uta4+uta5+uta6+uta7 mett.show() #3(c).LA FUNCIÓN MAS CERCANA ES LA AZUL
2*pi
#INTEGRAL DE LA FUNCIÓN PRINCIPAL. s=integral(h1(t),t,-pi,0)+integral(h2(t),t,0,pi)
s
7*pi + 1/4*pi^3
nor2=integral((w3(t))^2,t,-pi,pi)
nor2
pi