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aalyn [17]
3 years ago
13

Evaluate the line integral, where c is the given curve. c y3 ds,

Mathematics
1 answer:
postnew [5]3 years ago
5 0
Parameterizing \mathcal C by

\mathbf r(t)=(t^3,t)

with 0\le t\le2, we have

\mathrm ds=\|\mathbf r'(t)\|\,\mathrm dt=\sqrt{(3t^2)^2+1^2}\,\mathrm dt=\sqrt{9t^4+1}\,\mathrm dt

So

\displaystyle\int_{\mathcal C}y^3\,\mathrm ds=\int_{t=0}^{t=2}t^3\sqrt{9t^4+1}\,\mathrm dt
=\displaystyle\frac1{36}\int_0^236t^3\sqrt{9t^4+1}\,\mathrm dt
=\displaystyle\frac1{36}\int_{u=1}^{u=145}\sqrt u\,\mathrm du
=\dfrac{145^{3/2}-1}{54}
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3 years ago
The crew on a fishing boat caught 4 fish that weighed a total of 1,092 pound. The tarpon weighed twice as much as the amberjack
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ddddd

Let T be the weight of Tarpon

Let A be the weight of amberjack

Let W be the weight of white marlin

Let TU be the weight of Tuna

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Total weight = 1092

T + A + W + TU = 1092

The tarpon weighed twice as much as the amberjack

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W = 2 T

We know T is 2A  so W = 2(2A) = 4 A, W = 4A

The weight of the tuna was 5 times the weight of the Amber jack.

TU = 5A

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Replace it in our equation

T + A + W + TU = 1092

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12A = 1092

Divide both sides by 12

A = 91

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