Download - 2 p 2 3 t 2 t 2 t 2 t dt 2 t dt t - WebAssignwebassign.net/latex2pdf/7d4da00e48dc0a0c64b31e63a5774866.pdf · ... y=4sint, −π 2 ≤t≤ π 2. Then R C xy2ds = Rπ/2 −π/2 (4cost)(4sint)2

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Page 1: 2 p 2 3 t 2 t 2 t 2 t dt 2 t dt t - WebAssignwebassign.net/latex2pdf/7d4da00e48dc0a0c64b31e63a5774866.pdf · ... y=4sint, −π 2 ≤t≤ π 2. Then R C xy2ds = Rπ/2 −π/2 (4cost)(4sint)2

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