- #1

- 10

- 0

let

assuming x = 2*pi*v*t, why is E(t) multiplied by e^(-ix)?, i guess it has to do with the fact that it is the conjugate of e^(ix), but i can't figure it out

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- Thread starter QuantumDuality
- Start date

- #1

- 10

- 0

let

assuming x = 2*pi*v*t, why is E(t) multiplied by e^(-ix)?, i guess it has to do with the fact that it is the conjugate of e^(ix), but i can't figure it out

- #2

- 3,580

- 1,387

The second equation follows from first by taking the complex conjugate at each side of the first equation. And of course changing the name of the variable but I guess you know that ##\int f(x)dx=\int f(y)dy## no matter what x and y are.

- #3

- 10

- 0

f(x) = x³

y = x²

then

f(y) = (x²)³ = x⁶

dy/dx = 2x

dy = 2x dx

using the equation you suggest:

∫f(x)dx=∫f(y)dy

∫x³ dx=∫2x⁷ dx

i'm missing something?

- #4

- 3,580

- 1,387

What you doing is a change of variable ##y=x^2## in the integral ##\int\limits_{a}^{b}f(y)dy## so the interval of integration changes from ##(a,b)## to ## (\sqrt{a},\sqrt{b})##. So the last line of your post should be actually ##\int\limits_{a}^{b}x^3dx=\int\limits_{\sqrt{a}}^{\sqrt{b}}2x^7dx##.

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