Question 16 Find the Integral of a Vector-Value Function Let F(t) = (3t³ + 1,4e-st, 3 sin(2t)). Find F(t)dt (don't include the +C) S [F(t)dt = ( Question Help: Video Submit Question + C
Question 16 Find the Integral of a Vector-Value Function Let F(t) = (3t³ + 1,4e-st, 3 sin(2t)). Find F(t)dt (don't include the +C) S [F(t)dt = ( Question Help: Video Submit Question + C
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![## Find the Integral of a Vector-Valued Function
Let \(\vec{r}(t) = \langle 3t^3 + 1, 4e^{-5t}, 3 \sin(2t) \rangle\).
Find \(\int \vec{r}(t) dt\) (don't include the +C)
\[
\int \vec{r}(t) dt = \langle \, \_\_\_, \, \_\_\_, \, \_\_\_ \, \rangle + C
\]
**Help:**
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Transcribed Image Text:## Find the Integral of a Vector-Valued Function
Let \(\vec{r}(t) = \langle 3t^3 + 1, 4e^{-5t}, 3 \sin(2t) \rangle\).
Find \(\int \vec{r}(t) dt\) (don't include the +C)
\[
\int \vec{r}(t) dt = \langle \, \_\_\_, \, \_\_\_, \, \_\_\_ \, \rangle + C
\]
**Help:**
For assistance, you can watch the [Video](#).
**Submit:**
When you are ready, click the "Submit Question" button.
---
This content is designed to guide students through finding the integral of a vector-valued function, offering them both a structured problem to solve and a video resource for help.
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