In 39 and 40, the matrices are A(t) and B(t) are given.

Chapter 9, Problem 39E

(choose chapter or problem)

In Problems 39 and 40, the matrices $A(t) \text { and } B(t)$ are given. Find

$\int A(t) d t$

$\int_{0}^{1} B(t) d t$

$A(t)=\left[\begin{array}{ll} t & e^{t} \\ 1 & e^{t} \end{array}\right]$

$B(t)=\left[\begin{array}{ll} \cos t & -s i n t \\ \sin t & \cos t \end{array}\right]$

Equation Transcription:

$A(t)\ and\ B(t)$

$\int\limits_{\ }^{\ }A(t)\ dt$

$\int\limits_{0}^{1}B(t)\ dt$

$\frac{d}{dt}[A(t)B(t)]$

$A(t)=$ [ ${\ }_{\ 1\ \ \ {\ \ e}^{t}}^{\ \ t\ \ \ \ {\ e}^{t}\ }$ ]

$B(t)=$ [ ${\ }_{\ sin\ t\ \ \ \ \ cos\ t}^{\ \ cos\ t\ \ \ \ -sin\ t\ }$ ]

Text Transcription:

A(t) and B(t)

\int A(t) dt

\int 01B(t) dt

ddt[A(t)B(t)]

A(t)=[ 1 et t et ]

B(t)=[ sin t cos t cos t -sin t ]

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