Integral of cos²(x) - Step-by-Step Solution | ML for Beginners

Try the Calculator

Enter function to integrate:

∫ dx

Quick examples:

Solution

Answer:

Alternate form:

Step-by-Step Solution

Step 1

Use the power reduction formula: cos²(x) = (1 + cos(2x))/2

Step 2

Split the integral

Step 3

Integrate each term

Step 4

Simplify

🤖 Machine Learning Application

Like sin²(x), this integral is essential in Fourier transforms used by CNNs for image processing. Understanding these integrals helps in analyzing activation patterns in periodic neural network behaviors.

Frequently Asked Questions

What is the integral of cos²(x)?

The integral of cos²(x) is \frac{x}{2} + \frac{\sin(2x)}{4} + C, where C is the constant of integration.

How do you solve this integral?

Follow the step-by-step solution above, which uses standard integration techniques.

Where is this used in machine learning?

Like sin²(x), this integral is essential in Fourier transforms used by CNNs for image processing. Understanding these integrals helps in analyzing activation patterns in periodic neural network behaviors.