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5-14 Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 6.) g(x) = f* e²-¹ dt I 1 dt t³ + 1 5. g(x) = f*

5-14 Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 6.) g(x) = f* e²-¹ dt I 1 dt t³ + 1 5. g(x) = f*

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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I circled the problem I would like to be solved (it is number 6, please ignore numbers 5 and 7) *Please use handwriting not typing, I understand it better that way, thank you*
**5-14** Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 5. \( g(x) = \int_{1}^{x} \frac{1}{t^3 + 1} \, dt \) 6. \( g(x) = \int_{3}^{x} e^{t^2 - 1} \, dt \) 7. \( g(s) = \int_{5}^{s} (t - t^2)^8 \, dt \) --- **Explanation:** To find the derivatives of these functions using the Fundamental Theorem of Calculus, apply the theorem which states that if \( F(x) = \int_{a}^{x} f(t) \, dt \), then \( F'(x) = f(x) \).
Transcribed Image Text:**5-14** Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 5. \( g(x) = \int_{1}^{x} \frac{1}{t^3 + 1} \, dt \) 6. \( g(x) = \int_{3}^{x} e^{t^2 - 1} \, dt \) 7. \( g(s) = \int_{5}^{s} (t - t^2)^8 \, dt \) --- **Explanation:** To find the derivatives of these functions using the Fundamental Theorem of Calculus, apply the theorem which states that if \( F(x) = \int_{a}^{x} f(t) \, dt \), then \( F'(x) = f(x) \).
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