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Show all your work to receive full credit. Write your answers as complete sentences. 1. Integrate each of the following. a. [3x² e³x dx TU b. xcos(4x) dx

Show all your work to receive full credit. Write your answers as complete sentences. 1. Integrate each of the following. a. [3x² e³x dx TU b. xcos(4x) dx

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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**Calculus Practice Problems** *Instructions:* Show all your work to receive full credit. Write your answers as complete sentences. **1. Integrate each of the following.** a. \(\int 3x^2 e^{3x} dx\) b. \(\int_{0}^{\frac{\pi}{4}} x \cos(4x) dx\) In problem a, you are asked to integrate the function \(3x^2 e^{3x}\) with respect to \(x\). This requires the use of integration techniques, such as integration by parts or substitution, to find the antiderivative of the given function. In problem b, you are required to evaluate the definite integral of \(x \cos(4x)\) from \(0\) to \(\frac{\pi}{4}\). To solve this, you may also need to use integration techniques like integration by parts and then evaluate the resulting antiderivative at the given bounds.
Transcribed Image Text:**Calculus Practice Problems** *Instructions:* Show all your work to receive full credit. Write your answers as complete sentences. **1. Integrate each of the following.** a. \(\int 3x^2 e^{3x} dx\) b. \(\int_{0}^{\frac{\pi}{4}} x \cos(4x) dx\) In problem a, you are asked to integrate the function \(3x^2 e^{3x}\) with respect to \(x\). This requires the use of integration techniques, such as integration by parts or substitution, to find the antiderivative of the given function. In problem b, you are required to evaluate the definite integral of \(x \cos(4x)\) from \(0\) to \(\frac{\pi}{4}\). To solve this, you may also need to use integration techniques like integration by parts and then evaluate the resulting antiderivative at the given bounds.
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