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1. Find the derivative of each function using the FTC Part I arctant dt et b) dt (simplify your answer) t

1. Find the derivative of each function using the FTC Part I arctant dt et b) dt (simplify your answer) t

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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Please solve 1 (a) and (b), thanks!
**Calculus Exercise: Fundamental Theorem of Calculus and Integration Techniques** 1. **Find the derivative of each function using the FTC Part I** a) \(\frac{d}{dx} \int_{1}^{x^2} \arctan t \, dt\) b) \(\frac{d}{dx} \int_{\sqrt{x}}^{x} \frac{e^t}{t} \, dt\) (simplify your answer) 2. **Find the following definite and indefinite integrals. Use substitution when needed.** a) \(\int \sin \theta \cos^4 \theta \, d\theta\) b) \(\int \frac{e^{3x}}{e^{3x} + 2} \, dx\)
Transcribed Image Text:**Calculus Exercise: Fundamental Theorem of Calculus and Integration Techniques** 1. **Find the derivative of each function using the FTC Part I** a) \(\frac{d}{dx} \int_{1}^{x^2} \arctan t \, dt\) b) \(\frac{d}{dx} \int_{\sqrt{x}}^{x} \frac{e^t}{t} \, dt\) (simplify your answer) 2. **Find the following definite and indefinite integrals. Use substitution when needed.** a) \(\int \sin \theta \cos^4 \theta \, d\theta\) b) \(\int \frac{e^{3x}}{e^{3x} + 2} \, dx\)
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