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...
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![**Problem: Curve Length Calculation**
Find the length of the curve given by the polar equation:
\[ r = 1 - 2\sin\alpha \]
**Options:**
a. \( 13.95 \)
b. \( 13.36 \)
c. \( 12.50 \)
d. \( 13.55 \)
e. \( 13.23 \)
**Answer Choices:**
- \( \circ \) a
- \( \circ \) b
- \( \circ \) c
- \( \circ \) d
- \( \circ \) e
---
**Explanation:**
To solve this problem, you need to apply the formula for the length of a polar curve:
\[ L = \int_{\theta_1}^{\theta_2} \sqrt{ \left( \frac{dr}{d\theta} \right)^2 + r^2 } \, d\theta \]
Substitute the given equation for \( r \) and calculate the definite integral over the specified interval for \( \alpha \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa72e8965-bd79-4464-a740-a72095a0be2c%2F9bc90e31-7f9b-43f3-853d-915003dfaf34%2F9gvfkc6m_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem: Curve Length Calculation**
Find the length of the curve given by the polar equation:
\[ r = 1 - 2\sin\alpha \]
**Options:**
a. \( 13.95 \)
b. \( 13.36 \)
c. \( 12.50 \)
d. \( 13.55 \)
e. \( 13.23 \)
**Answer Choices:**
- \( \circ \) a
- \( \circ \) b
- \( \circ \) c
- \( \circ \) d
- \( \circ \) e
---
**Explanation:**
To solve this problem, you need to apply the formula for the length of a polar curve:
\[ L = \int_{\theta_1}^{\theta_2} \sqrt{ \left( \frac{dr}{d\theta} \right)^2 + r^2 } \, d\theta \]
Substitute the given equation for \( r \) and calculate the definite integral over the specified interval for \( \alpha \).
Expert Solution
Step 1
Given.
A curve is defined in parametric form such that.
r = 1-2sin(a)
We need to find the lenth of the curve
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