I know you’re supposed to change the bounds and break up the integral, but for some reason, I can’t get the 44/3. Can someone explain how to solve this definite integral?
Answers
First, look for the zeroes of the integrand in the interval [0, 6] :
x² - 6x + 8 = (x - 4) (x - 2) = 0 ⇒ x = 2 and x = 4
Next, split up [0, 6] into sub-intervals starting at the zeroes we found. Then check the sign of x² - 6x + 8 for some test points in each sub-interval.
• For x in (0, 2), take x = 1. Then
x² - 6x + 8 = 1² - 6•1 + 8 = 3 > 0
so x² - 6x + 8 > 0 over this sub-interval.
• For x in (2, 4), take x = 3. Then
x² - 6x + 8 = 3² - 6•3 + 8 = -1 < 0
so x² - 6x + 8 < 0 over this sub-interval.
• For x in (4, 6), take x = 5. Then
x² - 6x + 8 = 5² - 6•5 + 8 = 3 > 0
so x² - 6x + 8 > 0 over this sub-interval.
Next, recall the definition of absolute value:
[tex]|x| = \begin{cases}x & \text{for }x \ge0 \\ -x & \text{for }x < 0\end{cases}[/tex]
Then from our previous analysis, this definition tells us that
[tex]|x^2 - 6x + 8| = \begin{cases}x^2 - 6x + 8 & \text{for }0<x<2 \text{ or } 4<x<6 \\ - (x^2-6x+8) & \text{for }2<x<4\end{cases}[/tex]
So, in the integral, we have
[tex]\displaystyle \int_0^6 |x^2-6x+8| \, dx = \left\{\int_0^2 - \int_2^4 + \int_4^6\right\} (x^2 - 6x + 8) \, dx[/tex]
Then
[tex]\displaystyle \int_0^2 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_0^2 = \frac{20}3 - 0 = \frac{20}3[/tex]
[tex]\displaystyle \int_2^4 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_2^4 = \frac{16}3 - \frac{20}3 = -\frac43[/tex]
[tex]\displaystyle \int_4^6 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_4^6 = 12 - \frac{16}3 = \frac{20}3[/tex]
and the overall integral would be
20/3 - (-4/3) + 20/3 = 44/3
Related Questions
Find the center and radius of the circle with the equation: (x=5)2 +(4-2)3-25
Answers
Answer:
center = (5 ,-3) and radius = 5
Step-by-step explanation:
Can someone please explain step by step on how I get my answer of [30% of 15?]
Answers
Answer: 4.5
Step-by-step explanation:
30% is equal to 30/100, which is 0.3
If you times 0.3 by 15, you will get 30% of 15
Therefore the answer would be 0.3 x 15 = 4.5
[tex]f(x) = {x}^{3 } + {3x}^{2} - 9x + 5[/tex]
which of the following are roots of a polynomial function?
check all that apply
a[tex]1 - \sqrt{3} [/tex]
b
[tex]1 + \sqrt{3} [/tex]
c
[tex] - 5[/tex]
D
[tex]3 - \sqrt{2} [/tex]
E
[tex]3 + \sqrt{2} [/tex]
F
[tex]1[/tex]
Answers
Answer:
[tex]f(1) = {(1)}^{3} + 3 {(1)}^{2} - 9(1) + 5 \\ (x - 1) = 0 \rightarrow \: x = 1 \\\frac{{x}^{3 } + {3x}^{2} - 9x + 5}{x - 1} = {x}^{2} + 4x - 5 \\ (x + 5)(x - 1) = 0 \\ x = - 5 \: or \: x = 1 \\ \color{red}\boxed{x_{1} = 1} \\\color{yellow} \boxed {x_{2} = 1} \\ \color{green}\boxed{x_{3} = - 5} [/tex]
The answer would be C and F
Answer: 1 & -5
Step-by-step explanation
GUY HELP DID CLICK OF THE RIGHT ONE ?
Answers
Answer:
c
Step-by-step explanation:
it just is that's the right book
Simplify (2x + 5y) + (3x - 2y)
Answers
Answer:
5x + 3y
Step-by-step explanation:
Combine Like terms: 2x + 3x = 5x
5x + (5y - 2y) = 3y
Ans: 5x + 3y
Joshua cashed a check for $16.79he asked the teller to give him as many quarters as possible .how many quarters did he get
Answers
Answer:
67 quarters
Explanation:
Apply the zero product property to solve the equation below:
x (x + 2) = 0
Answers
Answer:
0(-2+2)=0
Step-by-step explanation:
x=0
x=-2
0(-2+2)=0
Divide 63.5 ÷ 0.25 round the quotient to the nearest ten-thousandth
Answers
Answer:
254
Step-by-step explanation:
63.5 ÷ 0.25 =
= 63.5 ÷ 1/4
= 63.5 × 4
= 254
Answer: 254.
Karen, Trey, and Dante have a total of 75 in their wallets. Karen has 5 more than Trey. Dante has 2 times what Karen has. How much do they have in their wallets?
Answers
Answer: Karen has 20, Trey has 15, Dante has 40
Step-by-step explanation:
Karen=x+5 Trey=x Dante=2x+10
x+x+5+2x+10=75
4x+15=75
4x=60
x=15
9x2+8x(5x-4) simplify
Answers
Therefore, -14x + 40x² is the answer.
Hoped this helped.
[tex]-BrainiacUser1357-[/tex]
SOEMONE PLEASE TELL ME DID I CLICK THE RIGHT ONE
PLEASE PLEASE HELP ME
Answers
Answer:
Yes.
Step-by-step explanation:
I had a problem just like this and you are correct.
please help me on this
Answers
Answer:
10/9
Step-by-step explanation:
Malika knows that 230 - 39 = 191.
How can she use that to help her solve 233 - 42 = ?
Use the space and/or the lines below to answer.
Answers
Answer:
she has to minus just as she did before.
Step-by-step explanation:
230-39=191
233-42=191
the reason as to why they have the same answer is because it was first 230 but it later it was 233.so just minus as before.hope it will help goodbye
Answer:
See below
Step-by-step explanation:
She knows the answer is the same because both numbers are 3 higher than the other. She doesn't need to do anything.
What is 8 hours and 37 minutes converted into minutes?
Answers
Answer:
517 minutes
Step-by-step explanation:
Hope this helps:))
Answer:
517 mins
Step-by-step explanation:
1hour=60min
8hour=480min
37min is the same because it is already in minutes
480+37=517mins
what is the expression to 50 times the sum of 64 and 36
Answers
Answer:
50(64+36) this would be your answer
50 x (64+36)
Step-by-step explanation:
According to PEMDAS, you will have to solve 64 + 36 first, so you need to put them in the parenthesis. Next, simply multiply by 50.
Write each expression in terms of sine and cosine, and then simplify so that no quotients appear in the final expression and all functions are of x only.
[tex]\frac{csc^2 (-x)-1}{1-cos^2 (-x)}[/tex]
Answers
[tex]\stackrel{\textit{reciprocal ident.}}{csc(\theta)=\cfrac{1}{sin(\theta)}} ~\hfill \stackrel{\textit{symmetry ident.}}{sin(-\theta )=-sin(\theta)}~\hfill \begin{array}{llll} \stackrel{\textit{pythagorean ident.}}{sin^2(\theta)+cos^2(\theta)=1}\\ sin^2(\theta)=1-cos^2(\theta)\\ cos^2(\theta)=1-sin^2(\theta) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\cfrac{csc^2(-x)-1}{1-cos^2(-x)}\implies \cfrac{~~\frac{1}{sin^2(-x)}-1~~}{sin^2(-x)}\implies \cfrac{~~ \frac{1-sin^2(-x)}{sin^2(-x)}~~}{\frac{sin^2(-x)}{1}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{keeping in mind that}~\hfill }{sin^2(-x)\implies [sin(-x)]^2\implies [-sin(x)]^2\implies [sin(x)]^2\implies sin^2(x)} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{~~ \frac{1-sin^2(x)}{sin^2(x)}~~}{\frac{sin^2(x)}{1}}\implies \cfrac{1-sin^2(x)}{sin^2(x)}\cdot \cfrac{1}{sin^2(x)}\implies \cfrac{cos^2(x)}{sin^2(x)}\cdot \cfrac{1}{sin^2(x)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill cot^2(x)csc^2(x)~\hfill[/tex]
Find the 57th term of the arithmetic sequence -13,-29,-47,….
Answers
Answer:
answer -909 photo with solution is attached
From the graph, which statement is correct if x^2 – 13x + 22 ≤ 0?
A) 2 ≤ x ≤ 11
B) –11 ≤ x ≤ –2
C) x ≤ 2 or x ≥ 11
D) x ≥ 2 or x ≤ 11
please only reply if you know the answer!!
Answers
Answer:
a
Step-by-step explanation:
(x-2)(x-11) less than or equal to 0
which means x is between 2 and 11 when it is less than 0
List all the factors of 40 from least to greatest. Enter your answer below,
using a comma to separate each factor,
Answer here
TI
SUBMIT
Answers
Answer:
1,2,4,5,8,10,20,40
Step-by-step explanation:
Have a nice day
it's C. y = 1/2x + 2
Answers
Answer: what are you asking im lost
Step-by-step explanation:
Write as the opposite of a square root. -3√5
Answers
Answer:
3x5² is the opposite of ur uestion
The value of -3√5 as the opposite of the square root is -75.
What is square root?The factor of a number that, when multiplied by itself, yields the original number is known as the square root of the number. Special exponents include squares and square roots. Think about the number 9. When the number 3 is multiplied by itself, the result is 9.
Given:
-3√5
The opposite of the square root is the square, so,
-3√5 = -3 × 5²
-3√5 = - 3 × 25
-3√5 = - 75
To know more about square root:
https://brainly.com/question/9459418
#SPJ2
Suppose the sample space for a probability experiment has 48 elements. If items from the sample space are selected without replacement, how many different ways can you select all of the items?
Answers
Answer:
56study hard watch your book for 20 minute and look....this is a hint
candy is 5 years older than one-third Liam's age .if candy is 16,how old is Liam
Answers
Answer:
33
Step-by-step explanation:
16-5=11
11×3=33
so yeah
Answer:
18
Step-by-step explanation:
Draw two lines with a slope of 1 / 2. What do you notice about the lines?
Answers
Answer:
The lines would be parallel.
Step-by-step explanation:
lines with the same slope are parallel.
last month, a store sent 2,014 emails to customers about sales. the number of e-mails sent the month before was 2,104. Use one of the symbols <, >, or = to compare the two numbers to compare the two numbers of e-mails sent. Explain how you used the digits to determine your answer
Answers
Answer:
Last month (2,014) = (2,014) Month before last month
Your answer would be 2,014 = 2,014
The digits are all the same. Therefore, I concluded that the numbers were the same. This means that a equal sign should be used.
Hope this helps. Pls mark brainliest. :S
Pratima attends dance classes every 6 days, singing
classes every 4 days, and yoga classes every 16 days. If
.
she does all three activities today, in how many days will
she do all the three activities again on the same day?
PLEASE SHOW YOUR WORK
Answers
Using the least common factor, it is found that she will do all the three activities again on the same day again in 48 days.
She sings every 4 days.She attends dance classes every 6 days.She has yoga classes every 16 days.To find how many days it takes so that she will do all the three activities again on the same days, we have to find the least common factor of 4, 6 and 16.
It is done factoring them using prime factors, then:
4 - 6 - 16|2
2 - 3 - 8|2
1 - 3 - 4|2
1 - 3 - 2|2
1 - 3 - 1|3
1 - 1 - 1
Hence:
lcm(4,6,8) = 2x2x2x2x3 = 48
She will do all the three activities again on the same day again in 48 days.
To learn more about the least common factor, you can take a look at https://brainly.com/question/25924269
Need some help in this please
Answers
Answer:
∠GHD is 85°
Step-by-step explanation:
180°-95°
85°
When h = π, the orange graph shifts
units to the
.
Answers
Answer: it shifts units to the right.when h=-π it shifts units to the left
Step-by-step explanation: positive pi goes to the right, negative to the left
y = 3 tan(x2 + 5) [using Chain Rule]
Answers
Answer:
6x sec2 (x2+5) the number to are in the top of x a c.
Market for flat-screen TVs:
Demand: Qd=2,600-5P
Supply: Qs=-1000 +10P
What would be the amount of shortage if a price ceiling is imposed at price of $205?
Your Answer: 1100
Answer
Answers
Answer:
525
Step-by-step explanation:
The demand at a price of 205 is ...
Qd = 2600 -5(205) = 2600 -1025 = 1575
The supply at a price of 205 is ...
Qs = -1000 +10(205) = 2050 -1000 = 1050
The demand exceeds the supply by ...
1575 -1050 = 525
The shortage is 525 units.