2 p 2 3 t 2 t 2 t 2 t dt 2 t dt t -...
1
Parametric equations for C are x = 4 cos t , y = 4 sin t , - π 2 ≤ t ≤ π 2 . Then C xy 2 ds = π/2 -π/2 (4 cos t)(4 sin t) 2 (-4 sin t) 2 +(4 cos t) 2 dt = π/2 -π/2 4 3 cos t sin 2 t 16(sin 2 t + cos 2 t) dt = 4 3 π/2 -π/2 (sin 2 t cos t)(4) dt =(4) 4 1 3 sin 3 t π/2 -π/2 = 2 · 4 4 3 = 512 3
Transcript of 2 p 2 3 t 2 t 2 t 2 t dt 2 t dt t -...
Parametric equations for C are x = 4 cos t , y = 4 sin t ,−
π2≤ t ≤ π
2. Then
∫
Cxy2 ds =
∫ π/2
−π/2(4 cos t)(4 sin t)2
√
(−4 sin t)2 + (4 cos t)2 dt
=∫ π/2
−π/243 cos t sin2 t
√
16(sin2 t+ cos2 t) dt
= 43∫ π/2
−π/2(sin2 t cos t)(4) dt = (4)4
[
1
3sin3 t
]π/2
−π/2
= 2 · 44
3= 512
3
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