Find the area of the region enclosed by the graphs of the functions
f(x)=x^2, g(x)=x^6
by partitioning the x- axis.
(Use symbolic notation and fractions where needed.)
Answers
Answer:
[tex]\displaystyle A = \frac{8}{21}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsFunctionsFunction NotationGraphingSolving systems of equationsCalculus
Area - Integrals
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
Step-by-step explanation:
*Note:
Remember that for the Area of a Region, it is top function minus bottom function.
Step 1: Define
f(x) = x²
g(x) = x⁶
Bounded (Partitioned) by x-axis
Step 2: Identify Bounds of Integration
Find where the functions intersect (x-values) to determine the bounds of integration.
Simply graph the functions to see where the functions intersect (See Graph Attachment).
Interval: [-1, 1]
Lower bound: -1
Upper Bound: 1
Step 3: Find Area of Region
Integration
Substitute in variables [Area of a Region Formula]: [tex]\displaystyle A = \int\limits^1_{-1} {[x^2 - x^6]} \, dx[/tex][Area] Rewrite [Integration Property - Subtraction]: [tex]\displaystyle A = \int\limits^1_{-1} {x^2} \, dx - \int\limits^1_{-1} {x^6} \, dx[/tex][Area] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle A = \frac{x^3}{3} \bigg| \limit^1_{-1} - \frac{x^7}{7} \bigg| \limit^1_{-1}[/tex][Area] Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle A = \frac{2}{3} - \frac{2}{7}[/tex][Area] Subtract: [tex]\displaystyle A = \frac{8}{21}[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Area Under the Curve - Area of a Region (Integration)
Book: College Calculus 10e
Related Questions
(f) 0.7 - 6.32 + (-0.8) + 1.28
Answers
Answer:
=0.7f−5.84
Step-by-step explanation:
Let's simplify step-by-step.
f(0.7)−6.32−0.8+1.28
=0.7f+−6.32+−0.8+1.28
Combine Like Terms:
=0.7f+−6.32+−0.8+1.28
=(0.7f)+(−6.32+−0.8+1.28)
=0.7f+−5.84
Answer:
=0.7f−5.84
Pls Brainliest
Write the equation of a line that passes through the point (1,4) and has a slope of 9.
Answers
Answer:
y=9x-5
Step-by-step explanation:
You want to find the equation for a line that passes through the point (1,4) and has a slope of 9.
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
To start, you know what m is; it's just the slope, which you said was 9. So you can right away fill in the equation for a line somewhat to read:
y=9x+b.
Now, what about b, the y-intercept?
To find b, think about what your (x,y) point means:
(1,4). When x of the line is 1, y of the line must be 4.
Because you said the line passes through this point, right?
Now, look at our line's equation so far: b is what we want, the 9 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specifically passes through the point (1,4).
So, why not plug in for x the number 1 and y the number 4? This will allow us to solve for b for the particular line that passes through the point you gave!.
(1,4). y=mx+b or 4=9 × 1+b, or solving for b: b=4-(9)(1). b=-5.The equation of the line that passes through the point (1,4) with a slope of 9
is
y=9x-5
Find y
A)10
B)2
C)15
D)4
Answers
Answer:
y = 4Step-by-step explanation:
3y = y + 8
3y - y = 8
2y = 8
y = 8÷2
y = 4
Answer:
4
Step-by-step explanation:
the regular price of a camera 180.00.the camera is on sale for 25% off the regular price.what is the sale price of the camera in dollars and cents
Answers
Step-by-step explanation:
180 decrease 25% =
180 × (1 - 25%) = 180 × (1 - 0.25) = 135
Hope this helps (:
Show work and explain how too find the answer please I’m not fully understand the question
Answers
Answer:
She would have 24 single shoes. This is because she has 12 pairs and there are 2 of something in each pair. Therefore, Danielle would have 24 single shoes. (12*2=24) Hope this helped!!
a teacher attempts to make a number cube unfair by drilling out the spots on one side and inserting lead weights. to determine if she was successful she rules the number cube 50 times and keeps track of the number of times she rolls a 1. she rolls a 1 15 times. She would like to know if the data provide convincing evidence that the proportion of roles will land on a one is greater than 1/6. are the conditions for inference met?
yes the conditions for infants are met
no, the 10% condition is not met
no, the large counts condition is not met
no the rain is condition is not met
Answers
Answer:
No, the Large Counts Condition is not met.
Step-by-step explanation:
edge 2021
The condition for inference met is no, the large count's condition is not met.
A teacher attempts to make a number cube unfair by drilling out the spots on one side and inserting lead weights. to determine if she was successful she rules the number cube 50 times and keeps track of the number of times she rolls a 1. she rolls a 1 15 times.
What is the interference?Interference is the phenomenon that occurs when two waves meet while traveling along with the same medium.
The interference of waves causes the medium.
She would like to know if the data provide convincing evidence that the proportion of roles will land on a one is greater than 1/6.
Therefore option second is correct.
That is no, the large count's condition is not met.
To learn more about the interference visit:
https://brainly.com/question/2166481
#SPJ2
What is the area of the rectangle above?
A.
14 square units
B.
28 square units
C.
44 square units
D.
33 square units
Answers
Answer:
A = 33 units^2
Step-by-step explanation:
The area of a rectangle is given by
A = l*w where l is the length and w is the width
A = 11 * 3
A = 33 units^2
Answer:
D. 33 square units
Step-by-step explanation:
A=wl=3x11=33
x is 16% of 31.25 what is the answer
Answers
Answer: 5
Step-by-step explanation:
Answer:
5
Step-by-step explanation: 31.25 X 0.16=5
Bags of flour at a local grocery store have a mean weight of 83 ounces with a standard deviation of 2 ounces. The manufacturer of the flour states that 5% or less of the bags are underweight. What is this weight?
Find the z-table here.
79.7 ounces
80.4 ounces
80.9 ounces
81.3 ounces
Answers
Answer:
80.4
Step-by-step explanation:
Need help on this question
Answers
Answer:
c Christopher
Step-by-step explanation:
hope this helps
In one house, a realtor decorates 4 twin beds and 1 queen bed with a total of 18 pillows.
In another house, she decorates 4 twin beds and 4 queen beds with a total of 36 pillows.
She puts the same number of pillows on each twin bed, and the same number of pillows on each queen bed.
How many pillows does she put on each twin bed?
How many pillows does she put on each queen bed?
Answers
Answer:
The answer would be 3 pillows on each twin bed and 6 pillows on each queen bed.
Step-by-step explanation:
first house:
3 pillows x 4 twin beds = 12 pillows
18 total pillows - 12 twin bed pillows = 6 queen bed pillows
Second house
6 queen bed pillows x 4 queen beds = 24 queen bed pillow
3 twin bed pillows x 4 twin beds = 12 twin bed pillows
24 queen bed pillow + 12 twin bed pillows = 36 total pillows
Answer:
3 pillows on each twin bed and 6 pillows on each queen bed.
Step-by-step explanation:
(i had this on khan and i already knew the answer just wanted to help :>)
Help fast please....
Answers
Answer:
a triangular prism
Step-by-step explanation:
they are all 180)
Answer:
Possibly pyramid and if it needs to be more specific triangular based pyramid.
Though this might not be correct.
Step-by-step explanation:
for calculating weighted mean of 64 patients with pulmonary tuberculosis by age group in Baghdad, find the arithmetic mean of the age of these patients, where Xj fj = 1660
Answers
Answer:
for calculating weighted mean of 64 patients with pulmonary tuberculosisfor calculating weighted mean of 64 patients with pulmonary tuberculosis by age group in Baghdad, find the arithmetic mean of the age of these patients, where Xj fj = 1660 by age group in Baghdad, find the arithmetic mean of the age of these patients, where Xj fj = 1660
Match each indicated measure in the first column for
⊙
O
⊙O.
Answers
Answer:
Step-by-step explanation:
By the property,
"Measure of the intercepted arc is double of the inscribed angle"
m(arc BC) = 2×48°
= 96°
By using the same property,
m(arc AC) = 2 × m(∠B)
m(∠B) = [tex]\frac{110}{2}[/tex]
= 55°
m(∠A) + m(∠B) + m(∠C) = 180° [Triangle sum theorem]
48° + 55° + m(∠C) = 180°
m(∠C) = 180° - 103°
= 77°
m(arc AB) = 2 × (m∠C)
= 2×77
= 154°
Which cylinder will have larger volume
Answers
Answer:wheres the photo at doe
Step-by-step explanation:
Find two consecutive whole numbers that √45 falls between.
Answers
A university class has 26 students: 12 are art majors, 9 are history majors, 5 and are nursing majors. The professor is planning to select two of the students for a demonstration. The first student will be selected at random, and then the second student will be selected at random from the remaining students. What is the probability that the first student selected is a history major and the second student is a nursing major?
Answers
Answer:
6.9%.
Step-by-step explanation:
Given that a university class has 26 students: 12 are art majors, 9 are history majors, 5 and are nursing majors, and the professor is planning to select two of the students for a demonstration, where the first student will be selected at random, and then the second student will be selected at random from the remaining students, to determine what is the probability that the first student selected is a history major and the second student is a nursing major the following calculations must be performed:
26 = 100
9 = X
9 x 100/26 = X
900/26 = X
34.61 = X
25 = 100
5 = X
500/25 = X
20 = X
0.2 x 0.3461 = X
0.069 = X
Thus, the probability that the first student selected is a history major and the second student is a nursing major is 6.9%.
Answer:
6.9%
Step-by-step explanation:
Hope this will help
The human retina contains cells called rods
and cones that absorb light and change it
to electric signals sent to the brain. There
are approximately 120,000,000 rods and
6,000,000 cones in a retina. How is the
number of rods in a human retina written
using scientific notation?
Answers
Answer:
H) 1.2 x 10^8
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
1.2 x 10^8
Plastic Rods
A factory makes rods by cutting plastic pipes that are 5 feet long into 8 rods.
Part A
How long is each rod?
40
feet
You may use the scratchpad to show your work.
Enter your answer as a fraction or a mixed number.
Part B
What is the total length of 13 rods?
Answers
Answer
65 feet long
Step-by-step explanation:
15x5 is 65
Answer:
Step-by-step explanation:
5 feet ÷ 8 = 5/8 of a foot for each rod.
(In inches that would be 5/8 × 12 inches = (5 × 12)/8 inches = 60/8 inches = 15/2 inches = 7 1/2 inches.)
13 rods would be 13 × 5/8 feet = (13 × 5)/8 feet = 65/8 feet = 8 1/8 feet
helpppppp ill give brainliest answer if you know
Answers
Answer:
16 in squared
Step-by-step explanation:
PLEASE HELP!!!! A diver is in a diving board located 11 feet above the surface of a pool. A swimmer is directly below the diver 4 feet below the surface of the pool. What is the difference between the height of the diver and the height of the swimmer?
Answers
Answer:
I think it is a 7 foot difference between both sorry if wrong
Can someone please help me
Answers
Answer:
So you must do tan(27)=x/2000Then once you have x you do: x^2+y^2=c^2 solve for c then add up all the sides and then subtract your total by 2000 to get the differenceeach Saturday morning Janie works 5 hours and earns $35.75. How much does Janie earn for each hour she works?
Answers
Answer:
$7.15
Step-by-step explanation:
You would get this by dividing $35.75 by 5.
try, check, and revise or write an equation to solve
What are the two whole numbers whose product is 294 and whose quotient is 6?
Answers
Answer: 7 and 42.
Step-by-step explanation:
Let the two whole numbers be x and y.
From the question given, we can form an equation as:
x × y = 294 ........ i
x/y = 6 .......... ii
From equation ii
x/y = 6
x = 6y
Put the value of x back into equation i
x × y = 294
6y × y = 294
6y² = 294
y² = 294/6
y² = 49
y = ✓49
y = 7
Since x × y = 294 and y = 7,
x = 294/7
x = 42
The numbers are 7 and 42.
Match the base to the corresponding height.
Base (b)
Height (h)
b.
b
h
h
b
Answers
Answer:
B. is the right answer
Step-by-step explanation:
Because I just know
Can someone help me with this question?
Answers
Answer:
m = 4
Step-by-step explanation:
[tex] \because ABCD\sim QRST[/tex]
[tex] \therefore \frac{10}{m}= \frac{15}{6}[/tex]
[tex] \therefore m= \frac{10\times 6}{15}[/tex]
[tex] \therefore m= \frac{60}{15}[/tex]
[tex] \therefore m=4[/tex]
wich expression is equivalent to 2,3/5 divided by 7/9
Answers
Answer:
117/35 is equalivent expression
Step-by-step explanation:
2 3/5 divided by 7/9
so you need to make 2 3/5 into a fraction
you do the denominator time the whole number plus the numerator to get 13/5
13/5 / 7/9
when you divided fractions you flip the seccond fraction and multiply to get....
13/5 times 9/7
so you do. 13 times 9 and 5 times 7
you get 117/35
Plzz help meee!
A. Break up the figure into a 2 ft by 3ſ it triangle and a 5 ft by § ft rectangle.
B.Break up the figure into a 2 ft by 5 ft triangle and a 5 ft by 3 ft rectangle.
C.Break up the figure into a 2 ft by § ft triangle and a 5 ft by § ft rectangle.
D.Break up the figure into a 2 ft by 13 ft triangle and a 5 ft by 3 ft rectangle.
Answers
Answer:
Step-by-step explanation:
Area is calculated by multiplying the length of a shape by its width. In this case, we could work out the area of this rectangle even if it wasn't on squared paper, just by working out 5cm x 5cm = 25cm² (the shape is not drawn to scale). Hope this helps
Order these numbers from least to greatest: 1.05, 0.95, 0.75, 1.01
Answers
Answer:
0.75 0.95 1.01 1.05
Step-by-step explanation:
Answer:
0.75,0.95,1.01,1.05
Step-by-step explanation:
Thats in order from smallest to biggest.
Hope this helped! If it did, please give me brainliest! That would help a lot! Thanks! :D
A packet has 54 sheets of paper. Suraj uses 4/9of the sheets. How many sheets has he used?
Answers
Answer:
Step-by-step explanation:
54(4/9)
216/9
24 sheets
Answer:
Suraj used 24 sheets of paper