Does anyone can proof the ∫ cos x dx = sin x + C?

[karakoos23]

Hi

Does anyone can proof the ∫ cos x dx = sin x + C?

Thanks in advance

 

[bunalmis]

Re: Integration problem

2Cos(x)=e^jx +e^-jx

2jSin(x)=e^jx -e^-jx

∫ cos x dx = 1/2 ∫ e^jx dx +1/2 ∫ e^-jx dx = =1/2j e^jx - 1/2j e^-jx + C = Sin(x) + C

Added after 1 hours 52 minutes:

∫ cos x dx = Sin(x) + C

d/dx (Sin(x) + C) = ?

d/dx Sin(x) = lim dx-->0 (1/dx) (Sin(x+dx) - Sin(x)) = lim dx-->0 (Sin(x)Cos(dx) +Sin(dx)Cos(x) - Sin(x))/dx

lim dx-->0 Sin(x)Cos(dx)/dx - Sin(x)/dx = 0

lim dx-->0 Sin(dx)Cos(x) /dx = cos(x)

d/dx Sin(x)=Cos(x)

 

[karakoos23]

Re: Integration problem

Hi bunalmis

Can you please tell me what title of textbook in which I can find that analysis of cosinus?

It would be much appreciated

 

[free1965tv]

Re: Integration problem

Wow

Added after 39 seconds:

2Cos(x)=e^jx +e^-jx

2jSin(x)=e^jx -e^-jx

∫ cos x dx = 1/2 ∫ e^jx dx +1/2 ∫ e^-jx dx = =1/2j e^jx - 1/2j e^-jx + C = Sin(x) + C

Added after 1 hours 52 minutes:

∫ cos x dx = Sin(x) + C

d/dx (Sin(x) + C) = ?

d/dx Sin(x) = lim dx-->0 (1/dx) (Sin(x+dx) - Sin(x)) = lim dx-->0 (Sin(x)Cos(dx) +Sin(dx)Cos(x) - Sin(x))/dx

lim dx-->0 Sin(x)Cos(dx)/dx - Sin(x)/dx = 0

lim dx-->0 Sin(dx)Cos(x) /dx = cos(x)

d/dx Sin(x)=Cos(x)

Wow