[tex] \sf \: please \: answer \: and \: do \: not \: spam[/tex]
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It's based on integrals....
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Answers
Hello Carousel!
[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]
Solve the integral.[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex] \tt \:\int \: \frac{ x + 2 }{( {x}^{2} + 3x + 3) \sqrt{x + 1}} \: dx \\ [/tex]
First, let's take I as ⇨ [tex]\tt \:\int \: \frac{ x + 2 }{( {x}^{2} + 3x + 3) \sqrt{x + 1}} \: dx \\ [/tex].
[tex]\tt \:I = \int \: \frac{ x + 2 }{( {x}^{2} + 3x + 3) \sqrt{x +1}} \: dx \\\tt \: I =\int \: \frac{ x + 2 }{( {x}^{2} + 2x + 1 + x + 2) \sqrt{x + 1}} \: dx \\ \tt \:I =\int \: \frac{ x + 2 }{( ({x + 1}^{2}) + x + 2) \sqrt{x + 1}}[/tex]
Let, x + 1 = m² => dx = 2mdm.
[tex]\tt \:I =\int \: \frac{ {m}^{2} + 1}{ {m}^{4} + {m}^{2} + 1 \cdot \: m} 2mdm \\ \tt \:I =\int \: \frac{ {m}^{2} + 1}{ {m}^{4} + {m}^{2} + 1 \cdot \: \bcancel{ m}} 2 \bcancel{m}dm \\ \tt \: I = \: \int \: \frac{ {m}^{2} + 1}{ {m}^{4} + {m}^{2} + 1 } 2dm[/tex]
Now, divide the numerator & denominator by m²....we'll get it as...
[tex]\tt \:I =2\int \: \frac{ 1 + \frac{1}{ {m}^{2} } }{ {m}^{2} + 1 + \frac{1}{ {m}^{2} } } \: dm \\\tt \: I =2\int \: \frac{ 1 + \frac{1}{ {m}^{2} } }{( {m}^{2} + \frac{1}{ {m}^{2} } - 2) + 3} \: dm \\\tt \: I =2\int \: \frac{ (1 + \frac{1}{ {m}^{2} }) \: dm }{ ({m} - \frac{1}{ m } ) ^{2} + 3} [/tex]
Now, let m - 1/m be t => (1 + 1/m²) dm = dt
[tex]\tt \:I =2\int \: \frac{ dt}{ {t}^{2} + 3 } \\ \tt \:I = 2\int \: \frac{ dt}{ {t}^{2} + ( \sqrt{3}) ^{2} }[/tex]
We know, [tex]\tt \:\int \: \frac{dx}{ {x}^{2} + a ^{2} } = \frac{1}{a} tan ^{ - 1} (\frac{x}{a} ) + c[/tex]...therefore...
[tex]\tt \:I = \frac{2}{ \sqrt{3} } {tan}^{ - 1} ( \frac{t}{ \sqrt{3} } ) + c \: \rightarrow \boxed{ \tt \: eq. \: 1}[/tex]
Now, substitute the value of 't' in eq. 1..we'll get..
[tex]\tt \:I = \frac{2}{ \sqrt{3} } {tan}^{ - 1} ( \frac{m - \frac{1}{m} }{ \sqrt{3} } ) + c \: \rightarrow \boxed{ \tt \: eq. \: 2}[/tex]
Now, substitute the value of 'm' in eq. 2...we'll get...
[tex] \tt \: I = \frac{2}{ \sqrt{3} } {tan}^{ - 1} ( \frac{ \sqrt{x + 1} - \frac{1}{ \sqrt{x - 1} } }{ \sqrt{3} } ) + c \\ \tt \:I = \frac{2}{ \sqrt{3} } {tan}^{ - 1} ( \frac{x + 1 - 1}{ \sqrt{3} \sqrt{x - 1} } ) + c \\ \boxed{\boxed{ \bf \: I = \frac{2}{ \sqrt{3} } {tan}^{ - 1} ( \frac{x }{ \sqrt{3 (x - 1} )} ) + c }}[/tex]
The correct answer is Option B.__________________
The question is really long & tricky but once you get the hang of it you'll be good. Good luck!__________________
Hope it'll help you!
ℓu¢αzz ッ
Related Questions
Can someone help me with this
Answers
-6 + x = -7
+6 +6 add 6 to both sides, 6's cancel out on the left.
________
x = -1, is the answer.
Hope this helps! Let me know if you have any other questions related to this problem. :)
Answer:
x= -1
Step-by-step explanation:
-6+x = -7
x = -7+6
x= -1
a triangle is equilateral if sides are the same length. true or false?
Answers
True
A triangle with all the three sides equal equilateral
Hope this helped you- have a good day bro cya)
the difference of complementary angles is 10 degree. find the measures of the angles.
Answers
Answer:
40° and 50°
Step-by-step explanation:
90=(x+10)+x
90=2x+10
80=2x
40=x
Therefore the answer is,
40 and 40+10
40° and 50°
Answer:
50° and 40°
Step-by-step explanation:
Complementary angles sum to 90°
let one angle be x then the other is x - 10
x + x - 10 = 90
2x - 10 = 90 ( add 10 to both sides )
2x = 100 ( divide both sides by 2 )
x = 50
x - 10 = 50 - 10 = 40
The angle measures are 50° and 40°
Can somebody pls help me I appreciate it
Answers
y=3-2x
please mark brainliest and have a nice day!
pls answer asap and correctly
Answers
Answer:
B
Step-by-step explanation:
Squares can not be rectangles, Rectangles always have 2 parallel line was longer or shorter then another two but squares' 4 line will always be the same length
There are 15 pieces of the same size candy in a bag. Four are banana flavored, three strawberry flavored, six cherry flavored, and two orange flavored. What would be the probability of picking a banana, cherry, or a strawberry flavored candy from the bag? Write your answer as a simplified fraction in a/b form.
Answers
Answer:
The answer is 7/15
Please help me solve this problem
Answers
Answer:
30
Step-by-step explanation:
If you subtract 30 - 12 you would get 18 and multiply by -3 would get you -54
how to calculate 9120 divided by 12 in long division
Answers
Answer:
use bus stop method to calculate.
By the way answer is 760
SOMONE HELP ME I HAVE
TO DO THIS AFTER SCHOOL PLS ASAP!!!
Answers
Answer:
1 no
2 I don't know
3 no
4 yes
5 2.5 is the slope
6 -0.5
7 no slope
Step-by-step explanation:
1 no because the y overlaps
2 not sure
3 it over laps
4 it never overlaps
5 y=2.5x-3
6 y=-0.5x+1
7 no slope it's just x=-2
for the 5-7 you can type that into demos and get more info
y=mx+b
m is the slope and b is y intercept
Which of the following intervals is equivalent to the statement -3
1. (-3,9]
2. [-3,9)
3. (-3,9)
4. [-3,9]
Answers
Answer: choice 3
Step-by-step explanation:
Find the equation of the line that passes through (-1,2) and is perpendicular toy=1−2x.Leave your answer in the formy=mx+c
Answers
0.810x0.00084/0.000400x0.0270leave the answer in a standard form
Answers
Answer:
4.5927 x 10^-2 ?
Step-by-step explanation:
A sunflower is 15 inches tall and grows 2 inches a week. How many weeks will it take for the
Sunflower to be 23 inches tall?
Need help making an equation!!
Answers
Answer:
4 weeks
Step-by-step explanation:
15 + 2x = 23
2x = 8
x = 4
the square root of negative 9 is not negative 3 because..
Answers
Answer:
You cant have a negative square root
Explanation:
The answers will always be positive or a perfect square
Hope this Helps
y times 7 then add t expression
Answers
Answer:
7y + t
Step-by-step explanation:
6. Write the following cubes in expanded form:
(iii) (3a + 4b)³
8. Evaluate the following cubes using suitable Identities:
(ii) (999)³
Answers
Answer:
Step-by-step explanation:
we can use this algebraic identity:
[tex](a+b)^{3} =a^{3} +b^{3} +3ab(a+b)[/tex]
So,[tex](3a+4b)^{3} =(3a)^{3} +(4b)^{3}+3(3a)(4b)(3a+4b)[/tex]
=[tex](3a+4b)^{3} =27a^{3} +64b^{3} +36ab(3a+4b)[/tex]
=[tex](3a+4b)^{3} =27a^{3} +64b^{3} +108a^{2} b+144ab^{2}[/tex]
[tex](999)^{3}[/tex]=[tex](1000-1)^{3}[/tex]
Now, we can use the following identity:
[tex](a-b)^{3} =a^{3} -b^{3} -3ab(a-b)[/tex]
=[tex](1000-1)^{3} =1000^{3} -1^{3} -3(1000)(1)(1000-1)\\[/tex]
[tex](1000-1)^{3} =1,000,000,000-1-2,997,000[/tex]
[tex](1000-1)^{3} =997,002,999[/tex]
PLEASE HELP WILL MARK BRAINLIEST
What is -100 represented in exponents
Answers
Step-by-step explanation:
[tex] { - 100}^{1} [/tex]
Due to the accuracy of the tape measure Avani used, the amount of foam needed to cover the play area is
.
Answers
Answer:
The length of Due to the accuracy of the tape measure Avani used, the play area is 7.5 meters. The width of the play area is the amount of foam needed to cover the play area is 5.3 meters.
Step-by-step explanation:
Answer:
39.8
Step-by-step explanation:
edge 2022
Solve for
x
x
−
1
3
=
6
Give your answer as an improper fraction.
Answers
Answer:
x
=
13
+
6
=
19
Step-by-step explanation:
this is so simple
Step-by-step explanation:
x=19 ayan na yung sagot huh
solve all these quick and brainliest answer
Answers
Answer:
a.
Step-by-step explanation:
25x^2-15x+25
=5(5x^2-3x+5)
b.
14xy-7x
=7x(2y-1)
5.a.
7x-4=24
or,7x=24+4
or,7x=28
or,x=28/7
therefore x=4
b.
4y+4=y+16
or,4y-y=16-4
or,3y=12
or,y=12/3
therefore y=4
Step-by-step explanation:
q 5)
a) as it's an Isosceles triangle so both the given sides are equal
so, a/q
→ 7x - 4 = 24
→ 7x = 24 + 4 = 28
→ x = 28/7 = 4
→ x = 4
therefore, value of x is 4.
b) 4y + 4 = y + 16
→ 4y - y = 16 - 4
→ 3y = 12
→ y = 12/3 = 4
→ y = 4
therefore, value of y is 4.
hope this answer helps you dear!
2) translation: 2 units up
Q(-4,-2), R(-4,-2), s(0, -2), t(-3-5)
Answers
Answer:
Q'(-4,0), R'(-4,1), S'(0,0), T'(-3,-3)
Step-by-step explanation:
To solve this, what we need to do is find out what the translation is. So if we are translating those coordinates up two units, then that means we are basically adding two to the y value.
So that means that we will use the mapping (x,y)→(x,y+2)
Now we plug this in. We will start with Q:
Q(-4,-2)→Q'(-4,-2+2)→Q'(-4,0)
So when Q is translated two units up, we get Q'(-4,0).
Now we will do R:
R(-4,-1)→R'(-4,-1+2)→R'(-4,1)
So when R is translated two units up, we get R'(-4,1).
Now we will do S:
S(0,-2)→S'(0,-2+2)→S'(0,0)
So when S is translated two units up, we get S'(0,0).
Next we will do T:
T(-3,-5)→T'(-3,-5+2)→T'(-3,-3)
So when T is translated two units up, we get T'(-3,-3).
Answer:
Step-by-step explanation:
Hello there !
[tex]\boxed{\begin{array}{c|c} \boxed{\bf x} & \boxed{\bf y+2} \\ -4 & 0 \\-4&1\\0\!\!\!\!&0 \\ -3 &-3 \end {array }}[/tex]
2. Evaluate: 6.231 x 10^3
Answers
Answer:
6.231 × 10³
= 6.231 × 1000
= 6231
Step-by-step explanation:
brainliest plz
Factorise; c cubed divided by c cubed?
HELP ASAP
Answers
Step-by-step explanation:
c³/c³ =1 .
hope this helps you.
Help me with this pls!!!
Answers
We can see that 2 pounds of pineapples is roughly worth $2.50.
To find the cost of 1 pound of pineapple, divide the cost by 2 and we will get $1.25.
pa answer po plss plssss
Answers
29/32
Step-by-step explanation:
ng x value 32wrffddfddfffryufcjhfddxhjhddxffdssdtt
Please Please Help Me
Answers
Answer:
Step-by-step explanation:
(4^29)
is the answer(s) E, D, C, B, or A?
Answers
Answer:
A,C,E
You can see that the temperature and heat energy is changing at those points than just sitting there like B and D
HELP ME PLEASE!! I"M TRYING :(
Answers
Answer:
3/8×4/5
= 3/10
...........
option a
Answer:
3/10Step-by-step explanation:
HOPE IT HELPS U!!!!When The sum of 1. 3240 and 1. 4872 is subtracted from 4. 0121 it will give you the difference of
A. 1. 2109
B. 2. 0905
C. 1. 2009
D. 2. 7009
Answers
Answer:
C. 1.2009
Step-by-step explanation:
1.3240 + 1.4872 = 2.8112
4.0121 - 2.8112 = 1.2009 - C
Please help my friend!!
Answers
Answer: 700
Step-by-step explanation: