The area of the shaded region under the curve y = 2 sin 2x in (a) equals the area of the shaded region under the curve y = sin x in (b). Explain why this is true without computing areas. y- 2 sin 2x 24 y sin x (b) Why do both regions have the same area? Choose the correct answer below. A. The area under a sine wave is always 2. Therefore, both curves have the same area. B. When the change of variables u = 2x is applied to the definite integral 2 sin 2x dx, the new integral evaluates to the same value as sin x dx from 0 to x. Oc. When the chain rule u = 2x is applied to the indefinite integral 2 sin 2x dx, the new integral evaluates to the same value as sin x dx from 0 to x. D. When the change of variables u = 2x is applied to the definite integral sin x dx, the new integral evaluates to the same value as 2 sin 2x dx, from 0 to x.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
icon
Related questions
icon
Concept explainers
Question
The area of the shaded region under the curve y = 2 sin 2x in (a) equals the area of
the shaded region under the curve y = sin x in (b). Explain why this is true without
computing areas.
y= 2 sin 2x
y sin x
(a)
(b)
Why do both regions have the same area? Choose the correct answer below.
A. The area under a sine wave is always 2. Therefore, both curves have the same area.
B. When the change of variables u = 2x is applied to the definite integral 2 sin 2x dx, the new
integral evaluates to the same value as sin x dx from 0 to x.
c. When the chain rule u = 2x is applied to the indefinite integral 2 sin 2x dx, the new integral
evaluates to the same value as sin x dx from 0 to .
D. When the change of variables u = 2x is applied to the definite integral sin x dx, the nev
integral evaluates to the same value as 2 sin 2x dx, from 0 to z.
Transcribed Image Text:The area of the shaded region under the curve y = 2 sin 2x in (a) equals the area of the shaded region under the curve y = sin x in (b). Explain why this is true without computing areas. y= 2 sin 2x y sin x (a) (b) Why do both regions have the same area? Choose the correct answer below. A. The area under a sine wave is always 2. Therefore, both curves have the same area. B. When the change of variables u = 2x is applied to the definite integral 2 sin 2x dx, the new integral evaluates to the same value as sin x dx from 0 to x. c. When the chain rule u = 2x is applied to the indefinite integral 2 sin 2x dx, the new integral evaluates to the same value as sin x dx from 0 to . D. When the change of variables u = 2x is applied to the definite integral sin x dx, the nev integral evaluates to the same value as 2 sin 2x dx, from 0 to z.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Application of Integration
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning