Use stokes' theorem to evaluate s curl f · ds. f(x, y, z) = 5y cos(z) i + ex sin(z) j + xey k, s is the hemisphere x2 + y2 + z2 = 4, z ≥ 0, oriented upward. step 1 stokes' theorem tells us that if c is the boundary curve of a surface s, then curl f · ds s = c f · dr since s is the hemisphere x2 + y2 + z2 = 4, z ≥ 0 oriented upward, then the boundary curve c is the circle in the xy-plane, x2 + y2 = 4 correct: your answer is correct. seenkey 4 , z = 0, oriented in the counterclockwise direction when viewed from above. a vector equation of c is r(t) = 2 correct: your answer is correct. seenkey 2 cos(t) i + 2 correct: your answer is correct. seenkey 2 sin(t) j + 0k with 0 ≤ t ≤ 2π.

By Stokes' theorem, the integral of the curl of across is equal to the integral of along the boundary of , call it . Parameterize by

with . So we have

he kicked it up? is this the answer ?

step-by-step explanation:

answer: (yeees, you need a poet.)

//blooming serenity//

beautiful in the morning

mysterious at night

wonderous nature souring

with all it's mystical might

the flower that blooms

to the fox that looms

nocturnal creatures

with various features

a blooming flower soon in sight

as a new little hatchling fears to take flight  

afraid to leave it's calming nest,

but dear little bird, mother knows best

as sure as there are stars in the sky,

life is not about who, where what, when or why-

it's the journey that follows

adventures we swallow

of   nature's deep wonders,

natural disasters and storm's thunders.

blooming serenity

life and nature, truly is heavenly.

-kerstien lehman

step-by-step explanation: