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Example Questions
Example Question #671 : Calculus Ii
Find the length of the following parametric curve
, , .
The length of a curve is found using the equation
We use the power rule
, where is a constant, to find and .,
In this case
The length of this curve is
Using the identity
Using a u-substitution
Let
and changing the bounds
Example Question #672 : Calculus Ii
Find the length of the following parametric curve
, , .
The length of a curve is found using the equation
, , .
We use the power rule
, where is a constant, to find and
In this case, the length of this curve is
Using the identity
using a u-substitution
and changing the bounds
Example Question #673 : Calculus Ii
Find the length of the following parametric curve
, , .
The length of a curve is found using the equation
We then use the following trigonometric rules,
and ,
where
and are constants.In this case
,
,
The length of this curve is
Using the identity
Using the trigonometric identity
where is a constant
Using the rule of integration for constants
Example Question #674 : Calculus Ii
Given
and , what is the arc length between
In order to find the arc length, we must use the arc length formula for parametric curves:
.
Given
and , we can use using the Power Rule for all
,
to derive
and
.
Plugging these values and our boundary values for into the arc length equation, we get:
Now, using the Power Rule for Integrals
for all
,
we can determine that:
Example Question #675 : Calculus Ii
Given
and , what is the arc length between ?
In order to find the arc length, we must use the arc length formula for parametric curves:
.
Given
and , wwe can use using the Power Rule for all
,
to derive
and
.
Plugging these values and our boundary values for into the arc length equation, we get:
Now, using the Power Rule for Integrals
for all
,
we can determine that:
Example Question #676 : Calculus Ii
Given
and , what is the arc length between ?
.
Given
and , we can use using the Power Rule for all
,
to derive
and
.
Plugging these values and our boundary values for into the arc length equation, we get:
Now, using the Power Rule for Integrals
for all
,
we can determine that:
Example Question #1 : Polar
Rewrite the polar equation
in rectangular form.
or
Example Question #2 : Polar
Rewrite in polar form:
Example Question #1 : Polar
Rewrite the polar equation
in rectangular form.
Example Question #671 : Calculus Ii
Give the polar form of the equation of the line with intercepts
.
This line has slope
and -intercept , so its Cartesian equation is .By substituting, we can rewrite this:
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