Integrating Vector-Valued Functions
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Evaluate the integral of
r
(
t
)
=
(
sinh
(
t
)
cosh
(
t
)
)
\textbf{r}(t) = \begin{pmatrix} \text{sinh}(t) \\ \text{cosh}(t) \end{pmatrix}
r
(
t
)
=
(
sinh
(
t
)
cosh
(
t
)
)
over
[
0
,
1
]
[0, 1]
[
0
,
1
]
.
QUESTION
Calculate the integral
r
(
t
)
=
(
3
t
4
)
\textbf{r}(t) = \begin{pmatrix} 3t \\ 4 \end{pmatrix}
r
(
t
)
=
(
3
t
4
)
over
[
1
,
3
]
[1, 3]
[
1
,
3
]
.
QUESTION
Evaluate the integral
r
(
t
)
=
(
t
t
2
)
\textbf{r}(t) = \begin{pmatrix} t \\ t^2 \end{pmatrix}
r
(
t
)
=
(
t
t
2
)
over
[
1
,
2
]
[1, 2]
[
1
,
2
]
.
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ANSWER
(
3
2
7
3
)
\begin{pmatrix} \textstyle\frac{3}{2} \\ \textstyle\frac{7}{3} \end{pmatrix}
(
2
3
3
7
)
. Integrate
t
t
t
to get
3
2
\frac{3}{2}
2
3
and
t
2
t^2
t
2
to get
7
3
\frac{7}{3}
3
7
over
[
1
,
2
]
[1,2]
[
1
,
2
]
.
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