True or False: If Cis given by x(t) =t and y(t) = t,0 < t < 1, then Ot?dt .Why or why not? %3| sphz |

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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How can i know the answer for this exercise? im learning about line integrals and got this question, but i'm not sure how to solve it.

True or False: If C is given by x (t) = t and y(t) = t,0 <t<1, then
zyds
Ot?dt . Why or why not?
%3D
Transcribed Image Text:True or False: If C is given by x (t) = t and y(t) = t,0 <t<1, then zyds Ot?dt . Why or why not? %3D
Expert Solution
Step 1

Definition of line integral:

The line integral of the function F on the curve C: rt=x(t), y(t) where atb is defined as,

CF ds=abFxt, y(t)x'(t)2+y'(t)2 dt

The given line integral is:

C xy ds

where C is the curve given as xt=t and yt=t0t1.

Hence, the given function F is:

F=xy

The given curve C is:

rt=xt, yt=t, t

where 0t1.

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