Integral of sinx cosx | Summary and Q&A

TL;DR

Learn three different techniques to find the integral of sine x cosine x.

Key Insights

• 😄 U substitution is a useful technique for simplifying integrals involving trigonometric functions.
• 💄 Making u equal to a trigonometric function can provide an alternative approach to finding the integral.
• 💁 The double angle formula for sine 2x can be utilized to rewrite the integral in a different form.
• 👻 The three different forms of the double angle formula for cosine 2x allow for multiple representations of the integral.

Transcript

in this video we're going to focus on finding the integral of sine x cosine x now there's three ways in which we can get the answer the first technique involves u substitution and we're going to replace u with sine x d u the derivative of sine is going to be cosine x dx and so let's substitute sine with the u variable and let's replace cosine x dx ... Read More

Questions & Answers

Q: What are the three methods for finding the integral of sine x cosine x?

The three methods are u substitution, making u equal to cosine x, and using the double angle formula for sine 2x.

Q: How does the u substitution method work?

In the u substitution method, you replace sine x with the variable u and cosine x dx with du. The integral becomes the integral of u du.

Q: How does the second method of making u equal to cosine x work?

By making u equal to cosine x, you can solve for dx by taking the derivative of cosine x. The integral becomes the integral of sine x u du divided by negative sine.

Q: What is the third method involving the double angle formula for sine 2x?

The third method replaces sine x cosine x with one-half sine 2x in the integral. You then find the antiderivative of sine 2x and divide it by 2.

Summary & Key Takeaways

• The first technique involves using u substitution by replacing sine x with the variable u and cosine x dx with du.

• The second technique involves making u equal to cosine x and solving for dx by taking the derivative of cosine.

• The third technique uses the double angle formula for sine 2x to replace sine x cosine x in the integral.