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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
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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**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.
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.
Expert Solution
Step 1: Determine the given variables

y equals 2 x to the power of negative 3 end exponent ; x equals 8 space t o space x equals t


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