1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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}
You might be interested in
Due at 11:59 P.M. Please Help
maw [93]

Answer:

multiply both sides by 30 in fraction form 30 / 30

& 570 for the blank square for numerator of 30

Step-by-step explanation:

8 0
3 years ago
8x + 6 - 2x = 34 x= ?
e-lub [12.9K]
8x + 6 - 2x = 34x

Simplify 8x +6 - 2x to 6x + 6:
6x + 6 = 34x

Subtract 6x from both sides:
6 = 34x- 6x

Simplify 34x - 6x to 28x:
6 = 28x

Divide both sides by 28:
\frac{6}{28} = x

Simplify \frac{6}{28} to \frac{3}{14} :
\frac{3}{14} = x

Now switch sides and the answer is:

x = \frac{3}{14}

:) <3

5 0
3 years ago
Read 2 more answers
Please help URGENT! WILL GIVE BRAINLEST AND 30 POINTS
ivanzaharov [21]

Answer:

The answer you are looking for is the letter B on your assignment hun. Merry almost Christmas☃️

5 0
3 years ago
Read 2 more answers
Hi can you help !!!???
GalinKa [24]

Answer:

C

Step-by-step explanation:

4 1/3 can be separated into 4, and 1/3.

half of 4 is 2.

Half of 1/3 is 1/6.

Add 2 and 1/6, and you get 2 and 1/6. Answer is C

5 0
2 years ago
Read 2 more answers
The figure below shows the distance between two cities on a map is 1/8 inch to 12 miles. ​
Paul [167]

Answer: A. 38.4

Step-by-step explanation:

Because...

12/3.75 is 3.2; 3.2× 12 is 38.4. do 12÷ 3.75 meaning 3.2 miles every hour multiplied by 12 to get 38.4 miles.

* Hopefully this helps:) Mark me the brainliest:)!!

<em>∞ 234483279c20∞</em>

3 0
3 years ago
Other questions:
  • A department store is having a 15% of sale on all winter coats you purchase a winter coat for 275. With 7.25% sale tax how much
    11·1 answer
  • Identify the minimum or maximum value and the domain and range of the function
    15·1 answer
  • Plese: 2+2.. My grandma doesn't believe me!
    6·2 answers
  • What is the equation of the graph below? A graph shows a parabola that opens up and crosses the x axis at negative two and negat
    7·2 answers
  • F(x) = 2^x<br><br><br> what is the domain ?<br> range ? asymptote ? and transformation
    15·1 answer
  • What is the slope of the function
    8·1 answer
  • Please help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! will give brainliest!!!!!!
    9·2 answers
  • What is an equation of the line that passes through the point (1,-3) and is perpendicular to the line x+3y=21?
    12·1 answer
  • What is the volume of a spherical shell with inner radius 7 and outer radius 8?
    13·1 answer
  • Kenneth works in a carpet store. The graph shows the proportional relationship between the amount of carpet in square feet, x, a
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!