<span>∫c F · dr
= ∫∫s curl F · dS, by Stokes' Theorem
= ∫∫ <2, 0, -x> · <-z_x, -z_y, 1> dA
= ∫∫ <2, 0, -x> · <1, 0, 1> dA, since z = 2 - x
= ∫∫ (2 - x) dA.
Since the region of integration is inside x^2 + y^2 = 9, convert to polar coordinates:
∫(r = 0 to 3) ∫(θ = 0 to 2π) (2 - r cos θ) * (r dθ dr)
= ∫(r = 0 to 3) (2 * 2π - 0) * r dr
= 2πr^2 {for r = 0 to 3}
= 18π.
</span>
Answer:
210 sq in
Step-by-step explanation:
Box dimensions: 5 x 5 x 8
2 faces: 5 x 5 -> 2 * 5 * 5 = 50
4 faces: 5 x 8 -> 4 * 5 * 8 = 160
Total = 50 + 160 = 210 sq in
Answer:
Wouldn't it just be 8?
Step-by-step explanation:
f(8)
8f^1-1
8f^0
8x1
8
