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
On the grid, draw the graph of<br> y = 2x - 3<br> for values of x from -2 to 4<br> Q
Pie

Answer:

Plot these points:(-2,-7) (-1,-5) (0,-3) (1,-1) (2,1) (3,3) (4,5)

Step-by-step explanation:

You need to substitute your x values into the x of the equation y=2(3)-3 to find the y value...

3 0
3 years ago
Tiana takes 3 hours to drive to the coast without stopping. How many minutes will it take her to reach the coast if she stops to
nika2105 [10]
3 hours is 180 minutes.

She rested for 20 additional minutes, thus it will take her 200 minutes.
8 0
3 years ago
Read 2 more answers
Knight and Haslam (2010) found that office workers who had some input into the design of their office space were more productive
sleet_krkn [62]

Answer:

1. Option A

2. Option A

Step-by-step explanation:

1.

The independent variable is the one which affects the other variable. Here two variables "design of office space" and "control by managers" control the  Productivity and well-being of the workers.

Hence, the independent variable is Control of the office manager

Option A

2. The dependent variable is the one which gets affected by the independent variable and in this case it is the Productivity and well-being of the workers.

Option A

5 0
2 years ago
Which of these is equal to cos 19°? A) sin 71° B) sin 81° C) cos 71° D) cos 81°
Over [174]
Cos α = sin (90-α) so cos 19 = sin 90-19 = sin 71
7 0
3 years ago
Read 2 more answers
Which coordinate pair fits the set of coordinates {(0, 4), (-2, 1), (-4, -2)} defined by a linearfunction?
dedylja [7]

Answer:

y = 1.5x + 4

Step-by-step explanation:

Slope = (y2-y2)/(x2-x1)

= (1-4)/(-2-0) = -3/-2 = 3/2

y = (3/2)x + c

When x=0, y=4 (y-intercept is 4)

y = (3/2)x + 4

y = 1.5x + 4

6 0
3 years ago
Other questions:
  • A two sided coin is flipped and a 6-sided number cube is rolled. Find P(tails,5)
    14·1 answer
  • What is the fraction of .375
    10·1 answer
  • a coach bought three soccer balls on sale. they normally sell for $26 each. they were on sale for $7 off the original price. the
    7·1 answer
  • in one week a kiln removes 1/3 of the moisture from a stack of wood. What fraction of the moisture remains in the lumber after 5
    5·1 answer
  • What is 94 written in word form
    6·2 answers
  • Stephen earns $17 an hour (h) at his job. This week, he had to buy a new uniform shirt for $25. He had $825 left of his paycheck
    10·1 answer
  • An inlet pipe can fill an empty swimming pool in 5hours, and another inlet pipe can fill the pool in 4hours. How long will it ta
    11·1 answer
  • PLEASE HELP ME WITH EMPIRICAL RULE!! ASAP!
    7·1 answer
  • HELP ASAP PLEASE
    6·1 answer
  • 15+25 distributive property
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!