Evaluate the line integral c f · dr, where c is given by the vector function r(t). f(x, y, z) = sin(x) i + cos(y) j + xz k r(t) = t4 i − t3 j + t k, 0 ≤ t ≤ 1

remember that

, or , and

parametizing

so

calculate

[/tex]<sin(t^4),cos(-t^3),t^5> \cdot <4t^3,-3t^2,1>=[/tex]

so evaluate integral

(using u subsitution with u=t^4 and for cosine, u=-t^3)

not sure if 1 is degrees or radians

this shows a reflection over the x-axis and is translated one unit down and 6 units to the right (x + 6, y - 1)

hope this !

~just a girl in love with shawn mendes

5

10

15

20

25

30

35

40

45

50

55