16.2 2.pdf - q  2 dx 2 dy dt x = t and y = 2t 0 ≤ t ≤ 2 so by C f(x y)ds = a f(x(t y(t dt dt p R2 2 R R 2 3√ R 2 3√ xy ds = h 0(t(2t(2t)2(2)2

# 16.2 2.pdf - q  2 dx 2 dy dt x = t and y = 2t 0 ≤ t ≤...

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Unformatted text preview: q  2 dx 2 + dy dt x = t and y = 2t , 0 ≤ t ≤ 2 , so by C f (x, y)ds = a f (x(t), y(t)) dt dt p R2 2 R R 2 3√ R 2 3√ xy ds = h 0 (t )(2t) (2t)2 + (2)2 dti= 0 2t 4t2 + 4 dt = 0 4t t2 + 1 dt C R 2 = = Rb Substitute u = t2 + 1 ⇒ t2 = u − 1 , du = 2t dt R5 R5 √ 2(u − 1) u du = 2 1 (u3/2 − u1/2 ) du = 1 √  √ √  2 10 8 2 5 − 5 − 5 = 1 + 25 + 2 50 5 3 5 3 15 5  2 25 u5/2 − 32 u3/2 1 ...
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