calc_tutorial_13_3_003

 
Problem Statement

{3,4,5,6,7,8,9}
pow(9,2)-1

Compute the length of the curve over the given interval.

r(t) = <2t, ln t, t2>, 1 ≤ t ≤ 9

 
Step 1

Question Sequence

Question 1

Recall how to find the length of a path for a vector-valued function r(t) = <x(t), y(t), z(t)>. Assume that r(t) is differentiable and that r'(t) is continuous on [a, b]. Then the length s of the path r(t) for a ≤ t ≤ b is defined as follows.

We will need r'(t) to find the length of the curve defined by r(t) = <2t, ln t, t2> on the interval 1 ≤ t ≤ 9.

Find r'(t).

r'(t) =

A.
B.
C.
D.
Correct.
Incorrect.

 
Step 2

Question Sequence

Question 2

Set up the integral that will give us the path length of r(t) = <2t, ln t, t2> on the interval 1 ≤ t ≤ 9.

A.
B.
C.
D.
Correct.
Incorrect.

 
Step 3

Question Sequence

Question 3

Factor the radicand to simplify the integrand.

A.
B.
C.
D.

=

A.
B.
C.
D.
Correct.
Incorrect.

 
Step 4

Question Sequence

Question 4

Integrate to find the length of the curve.

A.
B.
C.
D.

= + ln()

Correct.
Incorrect.