Find the area under the curve y = 2x -3 from x = 8 to x = t and evaluate it for t = 10, t = 100. Then find the total area under this curve for x ≥ 8. (a) t = 10 (b) t = 100 (c) Total area
Find the area under the curve y = 2x -3 from x = 8 to x = t and evaluate it for t = 10, t = 100. Then find the total area under this curve for x ≥ 8. (a) t = 10 (b) t = 100 (c) Total area
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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Transcribed Image Text:**Title: Calculating the Area Under a Curve**
To calculate the area under the curve defined by the equation \( y = 2x^{-3} \), we consider the interval from \( x = 8 \) to \( x = t \). We evaluate this for specific values of \( t \), namely \( t = 10 \) and \( t = 100 \). After evaluating these specific intervals, we find the total area under the curve for \( x \geq 8 \).
### Problem Statement
Find the area under the curve \( y = 2x^{-3} \).
1. **Evaluate the area from \( x = 8 \) to \( x = t \):**
- (a) For \( t = 10 \)
*Area Calculation Box*
- (b) For \( t = 100 \)
*Area Calculation Box*
2. **Total Area**
- (c) Find the total area under the curve for \( x \geq 8 \).
*Total Area Calculation Box*
This setup provides a systematic approach to calculating definite integrals for the function \( y = 2x^{-3} \) over specified intervals, as well as computing the total area for \( x \) values extending to infinity.
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