Integrating Vector-Valued Functions

Benjamin Wright

6 min read

Next Topic - Solving Motion Problems Using Parametric and Vector-Valued Functions

Study Guide Overview

This study guide covers integrating vector-valued functions. It explains how to integrate these functions component-wise in both two and three dimensions. It provides examples, including a walkthrough and a practice word problem involving velocity and position. The guide also briefly discusses the applications of integrating vector-valued functions, such as finding total area moved over time.

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Previous Topic - Defining and Differentiating Vector-Valued Functions Next Topic - Solving Motion Problems Using Parametric and Vector-Valued Functions

Question 1 of 9

Given the vector-valued function $r(t) = <t^3, \cos(t)>$ , what is the result of integrating only the first component with respect to t?

< $\frac{t^4}{4}$ , $\cos(t)$ >

$\frac{t^4}{4}$ + C

< $\frac{t^4}{4}$ +C , $\sin(t)$ +C>

< $t^4, \sin(t)$ >

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Integrating Vector-Valued Functions

Benjamin Wright

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