Find the area A of the region that is bounded between the curve f(x) = -4 sin () and the curve g(x) = -4 sin (x) over the interval [ ]. Enter an exact answer.
Find the area A of the region that is bounded between the curve f(x) = -4 sin () and the curve g(x) = -4 sin (x) over the interval [ ]. Enter an exact answer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem Statement:**
Find the area \( A \) of the region that is bounded between the curve \( f(x) = -4 \sin \left( \frac{x}{2} \right) \) and the curve \( g(x) = -4 \sin (x) \) over the interval \(\left[ \frac{\pi}{2}, \pi \right] \).
**Instructions:**
Enter an exact answer.
**Input Section:**
Provide your answer below:
\[ A = \boxed{\text{units}^2} \]
**Feedback Section:**
(There is a feedback button present here on the website for users to submit any issues or questions regarding the problem.)
**Note:**
This task involves finding the area between two curves over a specified interval. To solve this, one would typically use integration methods to find the area between the two curves \( f(x) \) and \( g(x) \) over the given interval \(\left[ \frac{\pi}{2}, \pi \right] \). This involves setting up and evaluating the definite integral of the absolute difference between the two functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4bc92d6f-8141-453b-b1aa-15dddf73f72d%2F25f5ae00-75c7-401e-8a7a-dd28201e61db%2Fga6vndc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the area \( A \) of the region that is bounded between the curve \( f(x) = -4 \sin \left( \frac{x}{2} \right) \) and the curve \( g(x) = -4 \sin (x) \) over the interval \(\left[ \frac{\pi}{2}, \pi \right] \).
**Instructions:**
Enter an exact answer.
**Input Section:**
Provide your answer below:
\[ A = \boxed{\text{units}^2} \]
**Feedback Section:**
(There is a feedback button present here on the website for users to submit any issues or questions regarding the problem.)
**Note:**
This task involves finding the area between two curves over a specified interval. To solve this, one would typically use integration methods to find the area between the two curves \( f(x) \) and \( g(x) \) over the given interval \(\left[ \frac{\pi}{2}, \pi \right] \). This involves setting up and evaluating the definite integral of the absolute difference between the two functions.
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