Answers
For the integral ∫asin(x)dx, use integration by parts ∫udv=uv−∫vdu.
Let u=asin(x) and dv=dx.
Then du=(asin(x))′dx=[tex]\rm \dfrac{dx}{ \sqrt{1 - {x}^{2} } } [/tex] and v=∫1dx=x
So,
[tex] \rm{\int{\operatorname{asin}{\left(x \right)} d x}}=\color{h}{\left(\operatorname{asin}{\left(x \right)} \cdot x-\int{x \cdot \frac{1}{\sqrt{1 - x^{2}}} d x}\right)}=\color{h}{\left(x \operatorname{asin}{\left(x \right)} - \int{\frac{x}{\sqrt{1 - x^{2}}} d x}\right)} \\ [/tex]
Let u=1−x2.
Then du=(1−x2)′dx=−2xdx and we have that xdx=−du/2.
The integral can be rewritten as
[tex] \rm x \operatorname{asin}{\left(x \right)} - \color{g}{\int{\frac{x}{\sqrt{1 - x^{2}}} d x}} = x \operatorname{asin}{\left(x \right)} - \color{j}{\int{\left(- \frac{1}{2 \sqrt{u}}\right)d u}} \\ [/tex]
Apply the constant multiple rule ∫cf(u)du=c∫f(u)du with c=-1/2 and f(u)=[tex] \frac{1}{ \sqrt{u} } [/tex]
[tex] \rm x \operatorname{asin}{\left(x \right)} - \color{h}{\int{\left(- \frac{1}{2 \sqrt{u}}\right)d u}} = x \operatorname{asin}{\left(x \right)} - \color{h}{\left(- \frac{\int{\frac{1}{\sqrt{u}} d u}}{2}\right)} \\ [/tex]
Apply the power rule
[tex] \rm\int u^{n}\, du = \frac{u^{n + 1}}{n + 1} \\ [/tex]
with n=−1/2
[tex] \rm x \operatorname{asin}{\left(x \right)} + \frac{\color{h}{\int{\frac{1}{\sqrt{u}} d u}}}{2}=x \operatorname{asin}{\left(x \right)} + \frac{\color{j}{\int{u^{- \frac{1}{2}} d u}}}{2}=x \operatorname{asin}{\left(x \right)} + \frac{\color{j}{\frac{u^{- \frac{1}{2} + 1}}{- \frac{1}{2} + 1}}}{2}=x \operatorname{asin}{\left(x \right)} + \frac{\color{j}{\left(2 u^{\frac{1}{2}}\right)}}{2}=x \operatorname{asin}{\left(x \right)} + \frac{\color{h}{\left(2 \sqrt{u}\right)}}{2} \\ [/tex]
[tex] \rm Recall \: that \: u=1− {x}^{2} [/tex]
[tex] \rm x \operatorname{asin}{\left(x \right)} + \sqrt{\color{re}{u}} = x \operatorname{asin}{\left(x \right)} + \sqrt{\color{rd}{\left(1 - x^{2}\right)}} \\ [/tex]
Therefore,
[tex] \rm\int{\operatorname{asin}{\left(x \right)} d x} = x \operatorname{asin}{\left(x \right)} + \sqrt{1 - x^{2}}+C \\ [/tex]
Related Questions
1. A point is a position, true or false
Answers
true true true true true true true
100 POINTS
The graph of f ′ (x), the derivative of f(x), is continuous for all x and consists of five line segments as shown below. Given f (0) = 6, find the absolute maximum value of f (x) over the interval [0, 5].
graph of line segments increasing from x equals negative 4 to x equals negative 3, decreasing from x equals negative 3 to x equals 0, increasing from x equals 0 to x equals 3, constant from x equals 2 to x equals 4 and decreases from x equals 4 to x equals 5. x intercepts at x equals negative 4, x equals 0, x equals 5
2
8
11
13
Answers
Area of a trapezoid = h(b2+b2)/2
Height of the trapezoid = 2
Base 1= 2
Base 2 = 4
Area of trapezoid from [0,4] = 6
Initial value: f(0)=7
Absolute Maximum F(x): 6 + 7 = 13
can I get help with this equation?(2√5-√6)(4√5-3√6)
Answers
Answer:
=58 - 10 (lil check thing) 30
Step-by-step explanation:
What are 2 equivalent ratios for 7:4
Answers
Answer:
14:8 and 21:12
Step-by-step explanation:
Equivalent fractions are fractions that look different but hold the same value. In this case, 7:4 = 14:8 = 21:12
Answer:
14:8, 28:16
Step-by-step explanation:
This could be anything. Ratios are like fractions; as long as you make changes to both sides, it will equal the same thing. So for the two examples I put, I simply multiplied both sides by 2 for the first one, and 4 for the second one.
But, you could multiply it by whatever you want, even negative numbers and fractions. However, I wouldn't try to complicate it, if the question didn't ask me to. Just keep to the easiest equivalents to make your life easier.
Hope this helps :))
a man purchased a used car for $1000. He decided to sell the car for 20% above his purchase price. He could not sell the car so he reduced his asking price by 20%. If he sells the car at the reduced price, will he have a profit or a loss or will he break even?
Answers
Answer:
ok so they purchased price of the car is $1000 and the asking price will be 20% of $1000 so $1000 is a 100% so to get 20% of $1000 it will be 100% + 20% to get 120 percent so the asking price is 120 per cent of $1000 so 120 percent of $1000 is equals to 1200 dollars then you are told that he could not sell it by that price so he reduced it by 20% so this $1200 is 100% so he reduced it by 20% so it will be 100% - 20% to get 80% so this person sold his car at 80% so we will get 80% of $1200 and we will get $960 so he made a loss of $40
20% above 1000 = 200, 1000 + 200 = 1200
20% below 1200 = 240, 1200 - 240 = 960
1000 - 960 = $40 loss
When a country imports more than its exports,it has a(n)
Answers
When a country imports more than how much it gives, it has a trade deficit.
Is this right I just need confirmation pls
Answers
Answer:
No
Step-by-step explanation:
The slope is -4/3, so it should start at y=8, then go down 4 and over (to the right) 3 units. So the next point would be (4, 3).
Please help I'll mark this as brainliest
Answers
Answer:
13/50
Step-by-step explanation:
26% of 100 is 26/100 as a fraction.
These can both be divided by 2.
Once you divide both by two you end up with 13/50.
Answer:
26 green marbles
Step-by-step explanation:
There are 100 marbles in the jar.
100 marbles are 100%
26% of these marbles are green.
Just as there are 100 marbles, we need to find how many marbles are green.
Let us do it like that: let a be the actual number of green marbles.
Marbles Percent
100 100%
a 26%
Let's find the ratio between 100% and 26% by doing 100/26 = 3.846153
We need to multiply 26 by 3.846153 in order to get to 100, right?
So same, I'll need to multiply a times 3.846153 in order to get 100.
3.846153 a = 100
divide both sides by 3.846153
a = 26 marbles
Therefore there are 26 green marbles.
Tell me if it helps you.
A grocery store bought yogurt for $2.20 per container and stored it in two refrigerators. During the night, one refrigerator malfunctioned and ruined 13 containers. If the remaining yogurt is sold for $3.94 per container, how many containers did the store buy if they made a profit of $105.38?
Answers
Answer:
96
Step-by-step explanation:
X be the total containers bought
Sales - cost = profit
4.08(X - 14) - 2.6X = 84.96
4.08X - 2.6X - 57.12 = 84.96
1.48X = 142.08
X = 96
Write 7/10 as a sum of fractions two different
ways.
Answers
Answer:
0.70, 70/100 and 14/20
Step-by-step explanation:
hope this helps
how to solve this w2-64= by facturing
Answers
Answer: (x+8)(x-8)
Step-by-step explanation:
hope this helped :)
Photo question to ask
Answers
Answer:
$205,625
Step-by-step explanation:
Total is x, so
16% * x = 32,900
x = 32,900/0.16 = 205,625
im confused on this, anyone have an idea what they mean?
Answers
Answer:
This looks like the perimeter formula for a rectangle :)
Step-by-step explanation:
I could be wrong but i hope this helps
Distributive property of 9 times 28
Answers
OR
9x(20+8)
Which formula gives the trade discount when the list price and single discount rate are given?
Question content area bottom
Part 1
A.
list price times single discount rate
B.
net price times single discount rate
C.
base equals portion times rate
D.
trade discount times single discount rate
Answers
Answer:
I believe it's
Step-by-step explanation:
A
however I could be wrong
What is the answer ?
x/y+17
If is x=12
and y=1/2
Answers
Answer:
jhhdh.duuemmeyyeymruur*
Write an addition, a multiplication, and a division statement with the
same answer
Answers
Answer:
5 x 5 = 25
20 + 5 = 25
50 ÷ 2 = 25
Step-by-step explanation:
Larissa had 25 feet of ribbon. She equally divided
all the ribbon to make 8 bows for gift boxes. How
many feet of ribbon were used for each bow?
Answers
Answer:
3 feet of ribbon
Step-by-step explanation:
Simply divide 25 by 8. Then you get 3 feet with a remainder of 1.
PLEASE HELP FIND THE AREA!
its pretty easy
Answers
Answer:
114 square meters
Step-by-step explanation:
I hope this helps! Have a lovely day!! :)
Jodha wants to tip the pizza delivery person 20%. If the cost of the pizzas is $15.99, what would be a reasonable amount to tip?
Answers
Answer:
$3.20
Step-by-step explanation:
20%-> .20
15.99*.20
Answer:
$3.20
Step-by-step explanation:
divide 15.99 by 100
[tex]\frac{15.99}{100}[/tex]=0.1599
you now have 1%of the cost
multiply by 20 to get 20%
0.1599*20=3.198
round to 2 decimal places to get the amount he will tip
3.20
Flora's Flower Shop is gearing up for Valentine's Day, which is typically their busiest time of the year. Flora was able to secure 9,000 red roses for the holiday this year. Flora sells red roses for $8 per stem, and bouquets of 12 red roses for $75. The cost per stem for Flora is $3. Typically half of all flowers are sold as individual stems and half as bouquets, however on Valentine's Day the majority of flowers are sold as part of bouquets. Last year Flora made $35,000 over the Valentine's Day holiday, and hopes to make the same profit this year. What is the maximum proportion of flower sales that can come from bouquets in order for Flora to earn a profit of $35,000. 42% O 50% 63% 81%
Answers
The maximum proportion of flower sales that can come from bouquets in order for Flora to earn a profit of $35,000 is A. 42%.
What is proportion?The proportion shows the ratios of two or more variables.
While the maximum proportion show the highest ratio or percentage of a variable required to equate an expression.
Data and Calculations:Number of red roses procured for sale = 9,000
Selling price per stem = $8
Selling price per bouquet (12 stems) = $75
Cost per stem = $3
Last year's Valentine Day profit = $35,000
Stem Boutique
Selling price $8 $75
Cost per stem 3 36 ($3 x 12)
Contribution margin per unit $5 $39 ($75 - $36)
Contribution margin per stem $5 $3.25 ($39/12)
Weighted contribution margin $22,500 $14,625 ($3.25 x 4,500)
Proportion 42% ($14,625/$35,000 x 100)
Thus, the maximum proportion of flower sales that can come from bouquets in order for Flora to earn a profit of $35,000 is A. 42%.
Learn more about proportions and ratios at https://brainly.com/question/12024093
Which graph represents the equation y = 1/3x +2
Answers
Answer:
No graph attached, but it would look like;
The y intercept (the line which meets the y axis) would be at positive 2,
it would then rise one and go over 3 to the right because they are both positive.
I need help with showing my work on converting 3 7/8
Answers
The answer is 31/8
3 is a whole number, right?
So we do:
8/8 + 8/8 + 8/8 + 7/8
We have 8/8 three times cuz we have 3 as the *whole* number
= 8 + 8 + 8 + 7= 31
Add the denominator = 31/8
Hope this helps :)
the lest than and greater than is similar off math
Answers
Answer:
?
Step-by-step explanation:
uhhh less than is x < y greater than is x > y
can you please provide more info!
Airlines have increasingly outsourced the maintenance of their planes to other companies. A concern voiced by critics is that the maintenance may be less carefully done so that outsourcing creates a safety hazard. In addition, flight delays are often due to maintenance problems, so one might look at government data on percent of major maintenance outsourced and percent of flight delays blamed on the airline to determine if these concerns are justified. This was done, and data from 2005 and 2006 appeared to justify the concerns of the critics. Do more recent data still support the concerns of the critics? Here are data from 2014:
Alaska 51.051.0 10.3510.35 Jet Blue 68.468.4 19.9319.93
American 29.429.4 20.3220.32 Southwest 58.258.2 28.4728.47
Delta 36.736.7 14.4814.48 United 52.652.6 23.4623.46
Frontier 46.346.3 21.4221.42 US Airways 54.354.3 13.6813.68
Hawaiian 78.478.4 5.065.06
Required:
a. Make a scatterplot with outsourcing percent as xx and delay percent as y.
b. Find the correlation r with and without Hawaiian Airlines.
Answers
Answer:
Please check attachment for graph
Step-by-step explanation:
B. With hawaii airline = -0.300
Without hawaii airline = 0.197
With hawaii airline
EX = 475.3
EY = 157.17
XY = 8042.11
X² = 26883.55
Y² = 3159.375
The correlation coefficient
= 72378.99-74702.9/7737.421
= -2323.91/7737.421
= -0.300
Without hawaii airline
EX = 396.9
EY = 152.11
EXY = 7645.406
X² = 20736.99
Y² = 3133.772
= 790.789/4021.161
= 0.197
The attendance for a basketball team declined at a rate of 5% per game throughout a losing
season. 23,500 people attended the first game. How many people attended the 8th game?
Equation:
Answer:
Answers
Answer:
y=23,500
Step-by-step explanation:
General form for an exponential equation
y = ab^{x - h} + k y=ab
or
y = ab^x y=ab
Exponential growth and decay, when the quantity increases by a fixed percentage at regular intervals.
Exponential growth y = a(1 + r)^x y=a(1+r)
\because b = (1 + r) ∵b=(1+r)
Exponential decay y = a(1 - r)^x y=a(1−r)
x
\because b = (1 - r) ∵b=(1−r)
Where, a - initial value
r - decay or growth rate
x - Number of time intervals that have passed
Step 2: Set up an exponential equation from the given in formation
Given that:
Declined(Decay) rate r = 5% = 0.05
Players from the first game a = 23,500
Exponential decay y = a(1 - r)^x y=a(1−r)
x
y=23,500(1-0.05)^xy=23,500(1−0.05)
x
y=23,500(0.95)^xy=23,500(0.95)
x
Step 3: Build a table of values by evaluating the function at different x-values.
y=23,500(0.95)^xy=23,500(0.95)
If x = 0 then y = 23,500(0.95)^x y=23,500(0.95)
y = 23,500(0.95)^0 y=23,500(0.95)
y = 23,500 * 1 y=23,500∗1
y=23,500
It takes 6 painters 4 half and hour to paint these classroom.
Is this direct or indirect proportion?
Give a reason for your answer
Answers
Answer:
Direct proportion
Step-by-step explanation:
In direct proportion, if one quantity is increased or decreased then the other quantity increases or decreases, respectively
A window has an actual height of 4.5 feet. If a blueprint has a scale of 3 inches = 2 feet, find the height of the window in the blueprint. Select one: 9 inches O 7.5 inches O 9.5 inches O 6.75 inches
Answers
2 feet: 3 inches
1 feet: 3/2 inches
4*5 feet: 3x4*5/2
=6.75 Inchea
Find the value of x and y. If necessary, round your answer to the nearest tenth. *
Answers
Answer:
Step-by-step explanation:
"y" is geometric mean ⇒ y² = 5 × 12
y = √60 ≈ 7.7
x² = 5² + ( √60 )²
x = √85 ≈ 9.2
If x = 6 and y= 4, evaluate the following expression:
3x^2 + 3xy + y^2
Answers
Answer:
plz refer the attachment
Answer:
3*6^2 + 3*6*4 + 4^2
18^2 + 72 + 4^2
324 + 72 + 16
412
Answer: 412