Question

Evaluate the integrals. $\int_{0}^{\pi} 3 \sin \frac{x}{3} d x$

   Evaluate the integrals.
$\int_{0}^{\pi} 3 \sin \frac{x}{3} d x$

Thomas Calculus

Thomas Calculus

George B. Thomas Jr. 14th Edition

Chapter 8, Problem 2

Instant Answer

Solved by Expert Enkhzaya Enkhtaivan

05/31/2019

Step 1

Let $u = \frac{x}{3}$. Then, $du = \frac{1}{3} dx$ and $dx = 3 du$. The limits of integration also change. When $x = 0$, $u = 0$ and when $x = \pi$, $u = \frac{\pi}{3}$. Show more…

Show all steps

lock

Thanks for your feedback!

Evaluate the integrals. $\int_{0}^{\pi} 3 \sin \frac{x}{3} d x$

Play audio

Feedback

Powered by NumerAI

Enkhzaya Enkhtaivan and 66 other subject Calculus 1 / AB 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

Definite Integral

A definite integral represents the computation of the area under the curve of a function between a lower and an upper limit. It is fundamental in calculus as it provides a numerical value that encapsulates the accumulation of quantities, such as areas or physical quantities like mass or charge, over a specified interval.

U-Substitution

U-substitution is a technique used in integration to simplify integrals by making a substitution that transforms the variable of integration. This method is particularly useful when dealing with functions composed with other functions, as it can reduce a complicated integral into a more straightforward form that is easier to evaluate.

Integration of Trigonometric Functions

Integrating trigonometric functions involves applying standard integration rules specific to sine, cosine, and other trigonometric functions. Understanding the antiderivatives of these functions, such as recognizing that the antiderivative of sine is negative cosine, is essential when solving integrals that involve trigonometric 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