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
iris [78.8K]
3 years ago
9

Find the area enclosed by the curve x = t2 − 2t, y = t and the y-axis.

Mathematics
1 answer:
MA_775_DIABLO [31]3 years ago
7 0
The curve hits the y-axis whenever x=0:

x=t^2-2t=0\implies t(t-2)=0\implies t=0,t=2

The area enclosed by the region is the sum of distances of every point on the curve where t\in[0,2] to the origin. This is given by the integral

\displaystyle\int_0^2\sqrt{x(t)^2+y(t)^2}\,\mathrm dt
\displaystyle\int_0^2\sqrt{(t^2-2t)^2+t^2}\,\mathrm dt
\displaystyle\int_0^2\sqrt{t^2(t-2)^2}\,\mathrm dt
\displaystyle\int_0^2|t||t-2|\,\mathrm dt

Since t\in[0,2], you have |t|=t and |t-2|=-(t-2)=2-t, giving you

\displaystyle\int_0^2(2t-t^2)\,\mathrm dt=t^2-\dfrac{t^3}3\bigg|_{t=0}^{t=2}=4-\dfrac83=\dfrac43
You might be interested in
Tony is making goody bags for her party each bag has six toys for pieces of candy and 12 stickers
Andrei [34K]

Number of bag = x

Then, number of candies & Strickers would be 6x & 12x respectively..


5 0
4 years ago
I really need help
nexus9112 [7]

Answer:

about $102.80

6 0
3 years ago
Read 2 more answers
A 30 ft wire stretches from the top of a light pole diagonally to the ground. The light pole is 10 feet high. What is the angle
suter [353]

Answer:

The correct answere would be 19 degrees after solving for the length of the wire plus the diagnal of the ground.

Step-by-step explanation:

8 0
3 years ago
MATH HELP ASAP!! MARKING BRAINLIEST
olga nikolaevna [1]

Answer:

-1, -7, -13, -19

Step-by-step explanation:

-2(-3)-7 =6-7= -1

-2(0)-7 =0-7= -7

-2(3)-7 =-6-7= -13

-2(6)-7 =-12-7= -19

7 0
3 years ago
Read 2 more answers
Confused number 17 and it got cut off but it says more than
snow_lady [41]
Hi!
The product of 67 and 9 is a little more than 600, because:
67 \times 9 = 603
Hope this helps! Good luck!!
6 0
3 years ago
Other questions:
  • Determine the product of each set of polynomials (2x-3)(4x+5)
    10·1 answer
  • Please please help ASAP please please I’ll mark you as a branlist
    14·1 answer
  • In order to figure out how much money she needs for her trip to the store, Jessica has to solve this equation,
    10·1 answer
  • Find the approximate area of the shaded region below, consisting of a right triangle with a circle cut out of it.
    7·1 answer
  • Throws?
    12·1 answer
  • {4x+10y=8<br>{4x+3y=22<br><br>x=<br>y=​
    13·1 answer
  • Write the equation of the line perpendicular to the line 2x - 5y = 7 and passes through the point (2, -3) in slope-intercept for
    11·1 answer
  • Help me with 7 and 9 show your work !
    11·1 answer
  • If f(x)=x³-3x²+5, what is f(2)? help:3<br><br>a. 1<br><br>b. 2<br><br>c. -1<br><br>d. -2
    10·1 answer
  • Two angles of a quadrilateral measure 126° and 199°. The other two angles are in a ratio of 2:3. What are the measures of those
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!