Find the area of the region bounded by the curves y = 1 − x 2 and y = x 2 − 1 from [ 0 , 1 ] .

Answers

Answer 1

The area of the region bounded by the curves y = 1 - x² and y = x² - 1 from [0, 1] is 4/3 square units.

To find the area of the region bounded by the curves y = 1 - x² and y = x² - 1 from [0, 1], we need to first identify the points of intersection between the curves. By setting y values equal, we get:

1 - x² = x² - 1
2 = 2x²
x² = 1
x = ±1

Since we're only concerned with the interval [0, 1], we can focus on the intersection point at x = 1. Next, we will set up an integral to calculate the area between the curves.

The area can be found by integrating the difference between the functions from 0 to 1:

Area = ∫(1 - x² - (x² - 1))dx from 0 to 1

Simplifying the integrand, we get:

Area = ∫(2 - 2x²)dx from 0 to 1

Now, we can integrate and evaluate:

Area = [2x - (2/3)x³] evaluated from 0 to 1

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

Thus, the area of the region bounded by the curves y = 1 - x² and y = x² - 1 from [0, 1] is 4/3 square units.

To know more about area, refer to the link below:

https://brainly.com/question/13252576#

#SPJ11


Related Questions

Which one is it???????

Answers

Answer:

up 6

mayby

.........

Answer:

Left 6 is the answer

Step-by-step explanation:

You must move it in the left to be able to solve it

Ten cards numbered 1-10 are placed in a hat.What is the probabiliy of randomly drawing a card with an even number then a card with a number equal to five if the firdt card iis replaced

Answers

Answer:

1/ 20

Step-by-step explanation:

Given :

Cards = {1,2,3,4,5,6,7,8,9,10}

Even number = {2,4,6,8,10}

Probability (drawing an even number) :

Number of even / total. Number of cards

5 / 10 = 1/2

Card with number, 5 :

P(card numbered 5) = 1/10

Since they are independent events :

P(even number) * P(card numbered 5)

1/2 * 1/10 = 1/20

I WILL MARK BRAINLYIST
Describe Programming Languages
Complete each sentence by choosing the correct answer from the drop-down menu.

The data type in a strongly typed language
before the variable can be used.
An example of a strongly typed language is

The data type in a weakly typed language
before the variable can be used.
An example of a weakly typed language is
.

Answers

Answer:

Complete each sentence by choosing the correct answer from the drop-down menu.

The data type in a strongly typed language  

has to be stated

before the variable can be used.

An example of a strongly typed language is  

JavaScript

.

The data type in a weakly typed language  

does not have to be stated

before the variable can be used.

An example of a weakly typed language is  

Python

.

Step-by-step explanation:

Theres no explanation just get the answers and say thanks lolololoo

Answer:

 

✔ has to be stated

✔ JavaScript

✔ does not have to be stated

 

✔ Python

Where are the black dots located?!!

Answers

-2, 2 and for the other 4,5

Answer:

(-2,2) ; (4,5)

Step-by-step explanation:

Do the points A(-2,1), B(-2,4), C(3, 4), D(3, 1) form a square?

Answers

Answer: i don't think they do

Step-by-step explanation: tell me if i wrong

No they form a rectangle because the sides are 3 and 5.
A squares has 4 equal sides. A rectangle has 2 opposite sides equal.

Please help quick will give brainliest!

Answers

Answer: Choice A) The linear equation, aka straight line

Explanation:

The end behavior is determined by the ratio of the leading terms. This is because for large x values, the leading terms "drown out" (so to speak) the weight of the other terms.

We divide the leading terms 10x^3 over 2x^2 to get 5x. So as x gets really large, in either the positive or negative direction, the tail end portions will start to approach y = 5x. This is the slant or oblique asymptote. The end behavior or y = 5x has the left side going down, while the right side is going up. The same applies for the f(x) function as well.

What is the value of 4 in 145,027

Answers

Answer:

40,000

Step-by-step explanation:

100,000 + 40,000 + 5,000 + 20 + 7 = 145,027

Which statement best describes the domain of the function represented in the graph?

Answers

Given:

The graph of a function.

To find:

The correct statement for the domain of the given function graph.

Solution:

Domain is the set of x-values for which the function is defined or it is the set  of input values.

From the given graph it is clear that it is a linear function with end points (1,2) and (9,14).

So, the given function is defined for [tex]1\leq x\leq 9[/tex]. Here 1 and 9 are including in the set of x-values.

Therefore, the correct option is C, i.e., [tex]1\leq x\leq 9[/tex] or x between 1 and 9, inclusive.

PLEASE HELP!!!!!!!!!!

Answers

Answer:

a = 30

b = 15

c = 3

d = 30

e = 10

f = 20

Step-by-step explanation:

60 deg and a + 30 are alt int <S and congruent

a + 30 = 60

a = 30

a + 30 and a + 2b are corresponding angles and congruent

a + 2b = a + 30

2b = 30

b = 15

a + 2b and 5b - 5c are vertical angles and congruent

5b - 5c = a + 2b

5(15) - 5c = 30 + 2(15)

75 - 5c = 30 + 30

75 - 5c = 60

-5c = -15

c = 3

a + 2b and 10c + d are corresponding angles and congruent

10c + d = a + 2b

10(3) + d = 30 + 2(15)

d + 30 = 60

d = 30

5b - 5c and 2d + 6e are supplementary and add to 180

5b - 5c + 2d + 6e = 180

5(15) - 5(3) + 2(30) + 6e = 180

75 - 15 + 60 + 6e = 180

6e + 120 = 180

6e = 60

e = 10

2d + 6e and 4f + 4e are alt int angles and congruent.

4f + 4e = 2d + 6e

4f + 4(10) + 2(30) + 6(10)

4f + 40 = 60 + 60

4f + 40 = 120

4f = 80

f = 20

Solve for x Round to the nearest 100th if needed.
x/13 + 18 = 49

Answers

x
--- + 18 = 49
13


x
--- = 49-18
13

x
--- = 31
13

x = 31×13

x = 403

Answer:

2.4

Step-by-step explanation:

X=49-18/13

X=31/13

X=2.38

Stewart has a home-based business putting on children’s parties. He charges $60 to design the party and then $6.00 per child. Write a function rule that relates the total cost of the party to the number of children n.


f(n) = 6 + 60n

f(n) = 6n – 55

f(n) = 60 + 6n

f(n) = 6 – 55n

Answers

Answer:

f(n) = 60 + 6n

Step-by-step explanation:

numbers of students = n

party decoration charge = 60

per child cost = 6

so, therefore

f(n) = 60 + 6n

MARK ME AS BRAINLISTPLZ FOLLOW ME

Answer: A. f(n) 60 + 6n

60 is constant

6 per child is variable

Let c = number of children

total cost = 60 +6c

Step-by-step explanation: i got it from somebody else's brainly

If there are n children, and each additional child who joins will add another $6 to the cost, then the cost due to the number of children will be 6n. We also have the fixed cost of $60, no matter how many children join. Therefore, we add up these costs to get Cost = f(n) = 60 + 6n.

The hypotenuse of the right triangle is 5y inches long. The lengths of the legs are x + 8 and x + 3 inches. If the perimeter of the triangle is 60 inches and the length of the hypotenuse minus the length of the shorter leg is 10 inches, how many inches long is the hypotenuse?

Answers

Answer:

25

Step-by-step explanation:

The perimeter of triangle is equal to the sum of all sides of triangle

then:

5y + (x+8) + (x+3) = 60

5y + 2x +11 = 60

5y +2x = 49  ..............................................................(1)

the hypotenuse - shorter leg = 10

hint (  shorter leg ) = x+3

then

5y - (x + 3 ) = 10

5y - x - 3 = 10

5y - x = 13               .................................................... (2)

from 1 and 2

5y +2x = 49  .................................................................. (3)

5y - x = 13 (multiply both sides by 2 )

10y - 2x = 26 ..................................................................(4)

by sum 3 and 4

15y = 75

then y = 75/15 = 5

then hypotenuse = 5y = 5 x 5 = 25

Answer:

5

Step-by-step explanation:


The average diameter of a tree is measured over time. The equation y = 3/4x, where x is time in years and y is the
diameter in inches, models this relationship.
What is the predicted diameter, in inches, of the tree after 12 years?

Answers

Answer:

The predicted diameter of a tree after 12 years is 9 inches.

Step-by-step explanation:

The average diameter of the tree is represented by [tex]y = \frac{3}{4}\cdot x[/tex]. The predicted diameter of the tree after 12 years is determined by evaluating the linear function at [tex]x = 12[/tex]. That is:

[tex]y = \frac{3}{4}\cdot (12)[/tex]

[tex]y = 9[/tex]

The predicted diameter of a tree after 12 years is 9 inches.

The table shows the number of tropical cyclones that formed during the hurricane
seasons over a 12-year period.
a. Find the probability to predict whether a future tropical cyclone in the Northern
Hemisphere is a hurricane. Round your answer to the nearest tenth.
about
%
b. Find the probability to predict whether a hurricane is in the Southern Hemisphere
Round your answer to the nearest tenth.
about
1%

Answers

Answer:

A.) is 46.2

B.) is 58.1

Step-by-step explanation:

What is the distance between (7,-3) and (4, -5)

Answers

Answer:

(3,2)

Step-by-step explanation:

The length of a rectangle is 5 centimeters more than the width.
The area of the rectangle is 36 square centimeters.
What is the length?

Answers

Answer:

Length is 4 centimeters

Step-by-step explanation:

4 x (4 + 5)

4 x 9

36

HELP PELASE ASAPppppp

Answers

Answer:

sin M = NK/MK = m/n

cos K = NK/MK = m/n

=> sin M/cos K = 1

What are the solutions of the quadratic equation p^2+3p-28=40

Answers

Answer:

the answer is  =-3±[tex]\sqrt{281}[/tex]/2

Step-by-step explanation:

Answer:

             [tex]\bold{p_1\approx6.88\ ,\qquad p_2\approx-9.88}[/tex]

Step-by-step explanation:

[tex]p^2+3p-28=40\\\\p^2+3p-68=0\\\\a=1\,,\ b=3\,,\ c=-68\\\\\\p=\dfrac{-3\pm\sqrt{3^2-4\cdot1\cdot(-68)}}{2\cdot1}=\dfrac{-3\pm\sqrt{281}}{2}\\\\p_1\approx6.88\ ,\qquad p_2\approx-9.88[/tex]

A line that includes the point (10,7) has a slope of 1. What is it's equation in slope-intercept form? ​

Answers

y=x-3 hope it’s right

please please please help asap

Answers

Answer:

∠ UVX = 126.8°

Step-by-step explanation:

∠ WVS and ∠ UVX are vertical angles and congruent, then

∠ UVX = 126.8°

HELP!!

Solve for x:
logx - log(x+5) = log2

need step-by-step solution

Answers

Answer:

no solution

Step-by-step explanation:

logx - log(x+5) = log2,

logx = log2 + log(x + 5),

Remember that logs of the same base can be added together by multiplying their arguments:

log(x) = log [(x + 5)*2]

We cancel the logarithms by taking the exponents of both sides:

x = (x + 5)*2,

x = - 10

But x = - 10 makes the value undefined, so we say no solution.

multiple choice geometry helPppp

Answers

Answer: D

Step-by-step explanation:

Use SOHCAHTOA

We are given the opposite of the angle and the hypotenuse. We can use the sine function to acquire the value of x°.

sin(x) = 7/13

Take the inverse sine on both sides by using a calculator to get:

x = 32.58°

Answer:

32.58° that the answer hope this helps

4 5/7 + 3 3/4 = ??
Simplify ur answer
Show ur work

Answers

Answer:

237/28

Step-by-step explanation:

4 5/7=33/7

3 3/4=15/4

----------------

33/7+15/4=132/28+105/28=237/28

Answer:

8 13/28 or as a decimal: 8.46

Step-by-step explanation:

Rewrite the sum:

(4+3)+(5/7+3/4)

Add the numbers 4+3:

7+(5/7+3/4)

Add the fractions:

7+41/28

Convert the improper fraction into a mixed number:

7 + 1 13/28

Write the mixed number as a sum of the whole number and the fractional part:

7+1+13/28

Add the numbers 7+1 and then there is your answer!

8 13/28

If your paper, quiz, homework, etc says decimal form or alternative form then the decimal form is 8.46 and the alternate form is 237/26. But 8 13/28 cannot be reduced any lower.

Please Help!

Which Triangles are similar and why?

Answers

Both because they are all the same triangle

help and ill give extra (60 points)

Answers

Answer:

1) substitution method

2) zero

Step-by-step explanation:

because it has no solution as the variables cancle out eachother.

Please help!!!

What is the missing value and why?

Answers

Answer:

11

Step-by-step explanation:

How tall is the bullding in the picture shown?
66 in.
36 ft
8 ft
4.36 ft
52.36 ft
24.75 ft
297 ft

Answers

Answer:

24.75FT

Step-by-step explanation:

The triangles in the picture are similar meaning that 36/8=4.5

66inches into ft = 3.5

3.5x4.5=24.75

Answer: C. 24.75 ft

Step-by-step explanation:

• Set up the proportion.

• Cross multiply.

• Complete the multiplication on the left side.

• Divide both sides by 100.

• Complete the divisions on both sides.

Which type of triangle is formed by joining three line segments with the following lengths?

8 in, 8 in, 8 in

Answers

Answer:

Equilateral Triangle

Step-by-step explanation:

Which series of transformations will create similar but not congruent figures? (1 point)
O reflection and translation
O reflection and dilation
O reflection and rotation
O rotation and translation

If you don't know let someone who does answer​

Answers

Answer:

I thik O rotation and translation

Please help :( I’m not understanding this question

Answers

Answer:

False

True

True

False

Step-by-step explanation:

Hope that helps!

Answer:

true false true true

Step-by-step explanation:

gd

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