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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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8_murik_8 [283]

Answer:

1

Step-by-step explanation:

There can be 0, 1 or infinitely many solutions. 0 if they are parallel and are different lines, 1 if the slopes are different, and infinitely many if they are the same line.

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Hope this helps Please mark as brainliest and have a blessed day

6 0
3 years ago
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For the answer to the question above, I'll explain my answer through an equation below.
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7 0
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A recent trend in advertising is viral marketing. The goal is to convince viewers to share an amusing advertisement by e-mail or
77julia77 [94]
I'm not sure what you are looking for but I'll answer this question based on what I think is needed.

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5 0
2 years ago
If there are 25 students in a class and 16 of them are girls, what percent of the students are girls? Please explain.
Kipish [7]

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7 0
3 years ago
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Someone please help asap, I will mark as brainliest. Thank you!!
defon

Answer:

the answer is c go ahead and click it

Step-by-step explanation:

8 0
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