Mixing
Calculus Integration of Arc Length
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Let $f(x)$ be a twice differentiable function over $[a,b]$ with arc length $L$. Show that there exists a value $c in [a,b]$ such that the angle $theta$ between the tangent line and the horizontal line at $x = c$ is given by $costheta = frac{b-a}{L}.$
I also know that $f'(a) = tan(theta)$ and that I need to apply the Mean Value Theorem.
calculus integration arc-length
asked Jan 21 at 19:10
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163
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add a comment |
$begingroup$
Let $f(x)$ be a twice differentiable function over $[a,b]$ with arc length $L$. Show that there exists a value $c in [a,b]$ such that the angle $theta$ between the tangent line and the horizontal line at $x = c$ is given by $costheta = frac{b-a}{L}.$
I also know that $f'(a) = tan(theta)$ and that I need to apply the Mean Value Theorem.
calculus integration arc-length
asked Jan 21 at 19:10
NOTMENOTME
163
$endgroup$
1
$begingroup$
As you say apply the MVT for integrals, $int_a^b g(x) , dx = g(c)(b-a)$, to the arc length integral.
$endgroup$
– RRL
Jan 21 at 20:51
add a comment |
$begingroup$
Let $f(x)$ be a twice differentiable function over $[a,b]$ with arc length $L$. Show that there exists a value $c in [a,b]$ such that the angle $theta$ between the tangent line and the horizontal line at $x = c$ is given by $costheta = frac{b-a}{L}.$
I also know that $f'(a) = tan(theta)$ and that I need to apply the Mean Value Theorem.
calculus integration arc-length
asked Jan 21 at 19:10
NOTMENOTME
163
$endgroup$
Let $f(x)$ be a twice differentiable function over $[a,b]$ with arc length $L$. Show that there exists a value $c in [a,b]$ such that the angle $theta$ between the tangent line and the horizontal line at $x = c$ is given by $costheta = frac{b-a}{L}.$
I also know that $f'(a) = tan(theta)$ and that I need to apply the Mean Value Theorem.
calculus integration arc-length
calculus integration arc-length
asked Jan 21 at 19:10
NOTMENOTME
163
asked Jan 21 at 19:10
NOTMENOTME
163
asked Jan 21 at 19:10
NOTMENOTME
163
asked Jan 21 at 19:10
NOTMENOTME
163
asked Jan 21 at 19:10
NOTMENOTME
163
163
1
$begingroup$
As you say apply the MVT for integrals, $int_a^b g(x) , dx = g(c)(b-a)$, to the arc length integral.
$endgroup$
– RRL
Jan 21 at 20:51
add a comment |
1
$begingroup$
As you say apply the MVT for integrals, $int_a^b g(x) , dx = g(c)(b-a)$, to the arc length integral.
$endgroup$
– RRL
Jan 21 at 20:51
1
1
$begingroup$
As you say apply the MVT for integrals, $int_a^b g(x) , dx = g(c)(b-a)$, to the arc length integral.
$endgroup$
– RRL
Jan 21 at 20:51
$begingroup$
As you say apply the MVT for integrals, $int_a^b g(x) , dx = g(c)(b-a)$, to the arc length integral.
$endgroup$
– RRL
Jan 21 at 20:51
add a comment |
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$begingroup$
As you say apply the MVT for integrals, $int_a^b g(x) , dx = g(c)(b-a)$, to the arc length integral.
$endgroup$
– RRL
Jan 21 at 20:51