Let f(x, y, z) = (5ex sin(y))i + (5ex cos(y))j + 7z2k. evaluate the integral c f · ds, where c(t) = 8 t , t3, exp( t ) , 0 ≤ t ≤ 1. (note that exp(u) = eu.)

I'm going to assume this reads

and the path is parameterized by

with . Under this parameterization,

and

Then in the integral,

(It's unlikely that an exact answer can be found in terms of elementary functions)

you didn't give me the choices, so i will just give you the graph so you can look at your choices and choose the right one.