Find the area under the curve Y=2x-3 from x = 8 to = 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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**Problem Statement:**

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 \( x \geq 8 \).

**Tasks:**

- (a) Evaluate for \( t = 10 \).  
  (Input box for solution)

- (b) Evaluate for \( t = 100 \).
  (Input box for solution)

- (c) Total area.
  (Input box for solution)

**Explanation:**

- This problem involves calculating the definite integral of the function \( y = 2x^{-3} \) over specified limits.
- The goal is to determine the area under the curve from \( x = 8 \) to \( x = t \) for given values of \( t \), and then to assess the total area as \( x \) approaches infinity.
Transcribed Image Text:**Problem Statement:** 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 \( x \geq 8 \). **Tasks:** - (a) Evaluate for \( t = 10 \). (Input box for solution) - (b) Evaluate for \( t = 100 \). (Input box for solution) - (c) Total area. (Input box for solution) **Explanation:** - This problem involves calculating the definite integral of the function \( y = 2x^{-3} \) over specified limits. - The goal is to determine the area under the curve from \( x = 8 \) to \( x = t \) for given values of \( t \), and then to assess the total area as \( x \) approaches infinity.
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