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

false.

step-by-step explanation:

false.

cavalieri's principle makes that statement about the volumes, not about the areas.

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2