Simple complex numbers integral

[elcotufa]

Homework Statement

Integrate using complex numbers
$$\int\limits_0^{2\pi} cos^4(\theta)$$

Homework Equations

$$cos^4(\theta)= (\frac{e^{j\theta} + e^{-j\theta}}2)^4$$

The Attempt at a Solution

$$<br /> \frac 1{2^4} (e^{j\theta} + e^{-j\theta})^4$$

I got
$$\frac 1{2^4} \int^{2\pi}_0 (e^{4j\theta}+4e^{2j\theta}+4e^{-2j\theta}+e^{-4j\theta}+6)$$

After this I am not sure what to do

The integral of $$\int e^{4j}$$ would be $$\frac{e^{4j\theta}}{4j}$$?

How do I cancel them?

Input appreciated

 

[Dick]

Homework Statement

Integrate using complex numbers
$$\int\limits_0^{2\pi} cos^4(\theta)$$

Homework Equations

$$cos^4(\theta)= (\frac{e^{j\theta} + e^{-j\theta}}2)^4$$

The Attempt at a Solution

$$<br /> \frac 1{2^4} (e^{j\theta} + e^{-j\theta})^4$$

I got
$$\frac 1{2^4} \int^{2\pi}_0 (e^{4j\theta}+4e^{2j\theta}+4e^{-2j\theta}+e^{-4j\theta}+6)$$

After this I am not sure what to do

The integral of $$\int e^{4j}$$ would be $$\frac{e^{4j\theta}}{4j}$$?

How do I cancel them?

Input appreciated

Sure, that's the integral of e^(4j*theta). You'll notice if you evaluate it from 0 to 2*pi the result is 0. The same for all the other exponentials. The only term that contributes is the 6.

 

[elcotufa]

thanks man