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h(x) = S*(8t³ + 2t)dt, use the FTC Part I to find h'(x). %3D

h(x) = S*(8t³ + 2t)dt, use the FTC Part I to find h'(x). %3D

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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The image contains the following mathematical problem: Given \( h(x) = \int_{1}^{x} (8t^3 + 2t) \, dt \), use the Fundamental Theorem of Calculus Part I to find \( h'(x) \). There is also writing in blue that reads "c 1 2 1." --- ### Explanation: The problem involves finding the derivative \( h'(x) \) using the Fundamental Theorem of Calculus Part I, which relates the derivative of an integral to the integrand itself when the limits of integration are variable. ### Blue Writing: The characters "c 1 2 1" appear written in blue, potentially indicating a step or reference related to the problem, but lacking further context in the image.
Transcribed Image Text:The image contains the following mathematical problem: Given \( h(x) = \int_{1}^{x} (8t^3 + 2t) \, dt \), use the Fundamental Theorem of Calculus Part I to find \( h'(x) \). There is also writing in blue that reads "c 1 2 1." --- ### Explanation: The problem involves finding the derivative \( h'(x) \) using the Fundamental Theorem of Calculus Part I, which relates the derivative of an integral to the integrand itself when the limits of integration are variable. ### Blue Writing: The characters "c 1 2 1" appear written in blue, potentially indicating a step or reference related to the problem, but lacking further context in the image.
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Step 1 : Analysis

Given : 

hx = ∫1x8t3 + 2tdt

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