Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question
**Problem Statement:** Find the area under the curve \( y = \frac{1}{6x^3} \) from \( x = 1 \) to \( x = t \) and evaluate it for \( t = 10 \), \( t = 100 \). Then find the total area under this curve for \( x \geq 1 \). **Options:** (a) \( t = 10 \) [Checkbox] (b) \( t = 100 \) [Checkbox] (c) Total area [Checkbox]
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Transcribed Image Text:**Problem Statement:** Find the area under the curve \( y = \frac{1}{6x^3} \) from \( x = 1 \) to \( x = t \) and evaluate it for \( t = 10 \), \( t = 100 \). Then find the total area under this curve for \( x \geq 1 \). **Options:** (a) \( t = 10 \) [Checkbox] (b) \( t = 100 \) [Checkbox] (c) Total area [Checkbox]
Expert Solution
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Step 1: Define the problem.

To find the area under the curve straight y equals fraction numerator 1 over denominator 6 straight x cubed end fraction space from space straight x equals 1 space to space straight x equals straight t 

and to evaluate it for straight t equals 10 comma space straight t equals 100. Then to find the total area 

under this curve for straight x greater or equal than 1.

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