Answer:
12
Step-by-step explanation:
<span>Let r(x,y) = (x, y, 9 - x^2 - y^2)
So, dr/dx x dr/dy = (2x, 2y, 1)
So, integral(S) F * dS
= integral(x in [0,1], y in [0,1]) (xy, y(9 - x^2 - y^2), x(9 - x^2 - y^2)) * (2x, 2y, 1) dy dx
= integral(x in [0,1], y in [0,1]) (2x^2y + 18y^2 - 2x^2y^2 - 2y^4 + 9x - x^3 - xy^2) dy dx
= integral(x in [0,1]) (x^2 + 6 - 2x^2/3 - 2/5 + 9x - x^3 - x/3) dx
= integral(x in [0,1]) (28/5 + x^2/3 + 26x/3 - x^3) dx
= 28/5 + 40/9 - 1/4
= 1763/180 </span>
3.06, 3 1/6, 3 3/4, 3.8.
Hope that helps.
Answer:
No
Step-by-step explanation:
x y
y = - 3(-2) + 1 = 7 -2 7
y = -3(0) +1 = 1 0 1
y = -3(1) + 1 = -2 1 -2
y = -3(3) + 1 = -8 3 -8
