Question

harish has been struggling to calculate the length of herical function defined as f(t)=(Cos,t,Sin t, t),for t =0 to t = 2pi . what do you think is the answer?​

Answer 1

Answer:

$2\sqrt{2} \pi}$

Step-by-step explanation:

Length of a curve is given by

$L=\int_0^{2\pi}\sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2+(\frac{dz}{dt})^2}$

$\implies L=\int_0^{2\pi}\sqrt{(\frac{d\cos t}{dt})^2+(\frac{d\sin t}{dt})^2+(\frac{dt}{dt})^2}$

$\implies L=\int_0^{2\pi}\sqrt{(-\sin t)^2+(\cos t)^2+(1)^2}$

$\implies L=\int_0^{2\pi}\sqrt{2}$

$\implies L=\sqrt{2} \times 2\pi$

$\implies L=2\sqrt{2} \pi$

I hopre this helps