Please answer number 2 , you can also help with number 1 if you dont mind. Thanks! 1. Find the length of the curve r(t) = (sin 2t, cos 2t) from t = 0 to t = 27.2. Find the length of the curve F(t) = (1+3t,4 + 2t*) from t = 0 to t = 1.

Answered: 1. Find the length of the curve r(t) =…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Please answer number 2 , you can also help with number 1 if you dont mind. Thanks!

1. Find the length of the curve r(t) = (sin 2t, cos 2t) from t = 0 to t = 27.
2. Find the length of the curve F(t) = (1+3t,4 + 2t*) from t = 0 to t = 1.

Expert Solution

Step

As we know that,

The expression for the length of vector-valued curve is:

$L = \int_{a}^{b} \sqrt{{(x' (t))}^{2} + {(y' (t))}^{2}} d t$

1).

Given:

$\vec{r} (t) = <\sin (2 t), \cos (2 t)>$ and $t = 0 t o 2 π$

So,

$x (t) = \sin (2 t), y (t) = \cos (2 t)$

And

$a = 0, b = 2 π$

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1. Find the length of the curve r(t) = (sin 2t, cos 2t) from t 0 to t = 2n. %3D 2. Find the length of the curve = (1+3t, 4+ 2t*) from t 0 to t 1.