Question

Evaluate the integrals in Exercises $1-22$ . $$\int \cos 2 x d x$$

   Evaluate the integrals in Exercises $1-22$ .
$$\int \cos 2 x d x$$

Calculus

George B. Thomas,… 12th Edition

Chapter 8, Problem 1

Instant Answer

Solved by Expert Christian Otero

07/22/2020

Step 1

We let $u = 2x$. This implies that $du = 2dx$ or $dx = \frac{1}{2}du$. Show more…

Show all steps

lock

Thanks for your feedback!

Evaluate the integrals in Exercises $1-22$ . $$\int \cos 2 x d x$$

Play audio

Feedback

Powered by NumerAI

Christian Otero and 78 other subject Calculus 2 / BC educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Indefinite Integral

An indefinite integral represents the antiderivative of a function, meaning it describes a family of functions whose derivative is the original function. It includes an arbitrary constant since differentiation of a constant yields zero.

Trigonometric Integration

Trigonometric integration deals with finding the antiderivatives of trigonometric functions, such as sine and cosine. Techniques often involve using known derivatives and trigonometric identities to simplify the integration process.

Substitution Method

The substitution method simplifies integration by letting a new variable represent a function of the original variable, effectively reducing a complex integral into a simpler standard form. This approach is particularly useful when the integrand is a composite function, as seen with functions like cosine of a multiple of x.

Chain Rule in Reverse

When integrating composite functions, the reverse application of the chain rule is used. Recognizing the inner function and its derivative helps in applying substitution effectively, making it easier to find the antiderivative of functions with nested expressions.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later