How do you find the length of the polar curve $r = θ$ $r=theta$ ?

Question

How do you find the length of the polar curve $r = θ$ $r=theta$ ?

1 Answer

Related questions

How do you find the arc length of a polar curve?
How do you find the exact length of the polar curve $r = e^{θ}$ $r=e^theta$ ?
How do you find the length of the polar curve $r = 5^{θ}$ $r=5^theta$ ?
How do you find the length of the polar curve $r = {cos}^{3} (\frac{θ}{3})$ $r=cos^3(theta/3)$ ?
How do you find the length of a petal of a polar curve?
How do you find the exact length of the polar curve $r = 3 sin (θ)$ $r=3sin(theta)$ on the interval $0 \leq θ \leq \frac{π}{3}$ $0<=theta<=pi/3$ ?
How do you find the exact length of the polar curve $r = 1 + sin (θ)$ $r=1+sin(theta)$ ?
What is the arclength of $r = \frac{3}{4} θ$ $r=3/4theta$ on $θ \in [- π, π]$ $theta in [-pi,pi]$ ?
What is the arclength of $r = 4 θ$ $r=4theta$ on $θ \in [- \frac{π}{4}, π]$ $theta in [-pi/4,pi]$ ?
What is the arclength of $r = cos θ - 3 sin 2 θ$ $r=costheta-3sin2theta$ on $θ \in [- \frac{π}{4}, π]$ $theta in [-pi/4,pi]$ ?

Impact of this question

10579 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-09-07T15:02:26

If $θ$ $theta$ goes from $θ_{1}$ $theta_1$ to $θ_{2}$ $theta_2$ , then the arc length of can be found by
$L = \int_{θ_{1}}^{θ_{2}} \sqrt{θ^{2} + 1} d θ$ $L=int_{theta_1}^{theta_2}sqrt{theta^2+1}d theta$ .

Since $r = θ$ $r=theta$ , which gives $\frac{d r}{d θ} = 1$ ${dr}/{d theta}=1$ , we have
$L = \int_{θ_{1}}^{θ_{2}} \sqrt{r^{2} + {(\frac{d r}{d θ})}^{2}} d θ = \int_{θ_{1}}^{θ_{2}} \sqrt{θ^{2} + 1} d θ$ $L=int_{theta_1}^{theta_2}sqrt{r^2+({dr}/{d theta})^2}d theta =int_{theta_1}^{theta_2}sqrt{theta^2+1}d theta$

Science

Math

Humanities

... and beyond

How do you find the length of the polar curve $r = θ$ $r=theta$ ?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find the length of the polar curve r=θr=theta ?

1 Answer

Related questions

Impact of this question

How do you find the length of the polar curve $r = θ$ $r=theta$ ?