Integral of sin^2(x)  Summary and Q&A
TL;DR
Learn how to integrate sine squared of x by using the identity sine squared x = (1  cosine 2x)/2 and simplifying the integral.
Key Insights
 π¨βπΌ The identity sine squared x = (1  cosine 2x)/2 is crucial in integrating sine squared x.
 π³ Breaking down the integral helps simplify the integration process.
 π¨βπΌ The integral of 1/2 dx simplifies to 1/2x, while the integral of cosine 2x dx simplifies to 1/4 sine 2x.
 π¨βπΌ Integrating sine squared x becomes easier when recognizing the derivative of cosine is sine, allowing for a direct integration.
 ποΈ Dividing the integral by the coefficient of x simplifies the integration process.
 πͺ It is important to understand the relationship between trigonometric identities and integration techniques in order to solve similar problems efficiently.
 βΊοΈ The video demonstrates how to integrate sine squared x stepbystep, providing a clear explanation of each stage.
Transcript
integrate sine squared of X solution in order to integrate sine squared of X it's useful to know a very important identity so the sine squared of X is equal to one minus cosine two x all divided by two so the first step in this problem is to rewrite sine squared using this identity so we can write it as one minus cosine two x all divided by two DX ... Read More
Questions & Answers
Q: What is the first step in integrating sine squared x?
The first step is to rewrite sine squared x as (1  cosine 2x)/2 using the identity.
Q: How do you break down the integral?
The integral is broken down into two parts: 1/2 times the integral of dx and 1/2 times the integral of cosine 2x dx.
Q: How do you integrate 1/2 dx?
The integration of 1/2 dx simplifies to 1/2x, as the derivative of x is 1.
Q: How do you integrate cosine 2x dx?
To integrate cosine 2x dx, you can use the identity: the integral of cosine x dx is equal to sine x + C. In this case, it becomes 1/4 sine 2x + C.
Summary & Key Takeaways

The first step is to rewrite sine squared x using the identity (1  cosine 2x)/2.

Break down the integral into two parts: 1/2 times the integral of dx, and 1/2 times the integral of cosine 2x dx.

The integration of 1/2 dx simplifies to 1/2x, and the integration of cosine 2x dx simplifies to 1/4 sine 2x.