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wel
3 years ago
6

Find the length of the curve. R(t) = 7t, 3 cos(t), 3 sin(t) , −2 ≤ t ≤ 2

Mathematics
1 answer:
Leviafan [203]3 years ago
8 0

we are given

r(t)=(7t,3cos(t),3sin(t))

we can find x , y and z

x=7t,y=3cos(t),z=3sin(t))

now, we can use arc length formula

L=\int\limits^a_b {\sqrt{(x')^2+(y')^2+(z')^2} } \, dt

now, we can find derivative

x'=7,y'=-3sin(t),z'=3cos(t))

now, we can plug values

and we get

L=\int _{-2}^2\sqrt{7^2+\left(-3\sin \left(t\right)\right)^2+\left(3\cos \left(t\right)\right)^2}dt

L=\int _{-2}^2\sqrt{7^2+9}dt

=\sqrt{58}\cdot \:2-\left(-2\sqrt{58}\right)

L=4\sqrt{58}...........Answer


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