?Evaluate the line integral.?C dx + ey dy 1 xz dz, C is given by r(t) = t4 i + t2 j + t3

Chapter 16, Problem 6

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QUESTION:

Evaluate the line integral.

C  dx + ey dy 1 xz dz,

C is given by r(t) = t4 i + t2 j + t3 k, 0 ⩽ t ⩽ 1

Questions & Answers

QUESTION:

Evaluate the line integral.

C  dx + ey dy 1 xz dz,

C is given by r(t) = t4 i + t2 j + t3 k, 0 ⩽ t ⩽ 1

ANSWER:

Step 1 of 2

To evaluate the integral

Here, is given by

                       (i)

Let the position vector of any arbitrary point on be

                                         (ii)

Then, on comparing equations (i) and (ii),

Now, differentiating w.r.t ,

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