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Practice: Area Under the Parametric Curve
Related Topics
Wize University Calculus 2 Textbook > Parametric & Polar Curves
Calculus w/ Parametric Curves
9 Activities
Practice Question
Write down the integral representing the area under the curve parameterized by
x
=
2
tan
t
x = 2\tan t
x
=
2
tan
t
,
y
=
2
t
y = 2t
y
=
2
t
, for
0
≤
t
≤
π
/
4
0 \le t \le \pi/4
0
≤
t
≤
π
/4
.
2
∫
0
π
/
4
sec
2
t
d
t
2{\displaystyle\int}^{\pi/4}_0\ \sec^2 t\de{t}
2
∫
0
π
/4
sec
2
t
d
t
∫
0
π
/
4
t
2
sec
2
t
d
t
{\displaystyle\int}^{\pi/4}_0t^2\ \sec^2 t\de{t}
∫
0
π
/4
t
2
sec
2
t
d
t
∫
0
π
/
4
t
sec
2
t
d
t
{\displaystyle\int}^{\pi/4}_0t\ \sec^2 t\de{t}
∫
0
π
/4
t
sec
2
t
d
t
4
∫
0
π
/
4
t
sec
2
t
d
t
4{\displaystyle\int}^{\pi/4}_0t\ \sec^2 t\de{t}
4
∫
0
π
/4
t
sec
2
t
d
t
4
∫
0
π
/
4
t
2
sec
2
t
d
t
4{\displaystyle\int}^{\pi/4}_0t^2\ \sec^2 t\de{t}
4
∫
0
π
/4
t
2
sec
2
t
d
t
I don't know
Check Submission
More Calculus w/ Parametric Curves Questions:
Practice: Area Under the Parametric Curve
Find the area under the curve
{
x
=
t
2
,
y
=
cos
t
:
t
∈
[
0
,
π
2
]
}
\left\{x=t^2,\ y=\cos t:\ t\in\left[0,\frac{\pi}{2}\right]\right\}
{
x
=
t
2
,
y
=
cos
t
:
t
∈
[
0
,
2
π
]
}
.
Practice: Area Under the Parametric Curve
Practice Question
Find the area under the cruve
{
x
=
t
2
,
y
=
cos
t
:
t
∈
[
0
,
π
2
]
}
\left\{x=t^2,\ y=\cos t:\ t\in\left[0,\frac{\pi}{2}\right]\right\}
{
x
=
t
2
,
y
=
cos
t
:
t
∈
[
0
,
2
π
]
}
.
Practice: Area Under the Parametric Curve
Practice Question
Find the area under the cruve
{
x
=
t
2
,
y
=
cos
t
:
t
∈
[
0
,
π
2
]
}
\left\{x=t^2,\ y=\cos t:\ t\in\left[0,\frac{\pi}{2}\right]\right\}
{
x
=
t
2
,
y
=
cos
t
:
t
∈
[
0
,
2
π
]
}
.
⭐ TRICKY!
Find, if possible, the maximum and minimum values of the curvature of the graph of
y
=
e
x
and the points at which they occur.