1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Liono4ka [1.6K]
3 years ago
8

Integrate 1/((x^5)*sqrt(9*x^2-1)) ...?

Mathematics
1 answer:
Korolek [52]3 years ago
5 0
Let 9x^2-1 = y^2 
<span>=> 18xdx = 2ydy </span>
<span>=> ydy = 9xdx </span>

<span>lower limit = sqrt(9*2/9 - 1) = sqrt(1) = 1 </span>
<span>upper limit = sqrt(9*4/9 - 1) = sqrt(3) </span>

<span>Int. [sqrt(2)/3,2/3] 1/(x^5(sqrt(9x^2-1)) dx </span>

<span>= Int. [sqrt(2)/3,2/3] xdx/(x^6(sqrt(9x^2-1)) </span>
<span>= 81* Int. [1,sqrt(3)] ydy/((y^2+1)^3y) </span>
<span>=81* Int. [1,sqrt(3)] dy/(y^2+1)^3 </span>

<span>y=tanz </span>
<span>dy = sec^2z dz </span>

<span>=81*Int [pi/4,pi/3] cos^4(z) dz </span>
<span>=81/4*int [pi/4,pi/3] (1+cos(2z))^2 dz </span>
<span>=81/4* Int. [pi/4,pi/3] (1+2cos(2z)+cos^2(2z)) dz </span>

<span>=81/4*(pi/3-pi/4) + 81/4*(sin(2pi/3)-sin(pi/2)) + 81/8 * (pi/3-pi/4) </span>
<span>+ 81/32 *(sin(-pi/3)-sin(pi)) </span>
<span>=81(pi/48+pi/96+1/4*(sqrt(3)/2 - 1) - 1/32 * sqrt(3)/2) </span>
<span>=81/32*(pi+3sqrt(3)-8)</span>
You might be interested in
Which equation is y = –3x2 – 12x – 2 rewritten in vertex form?
Andrej [43]
<span>The general equation of a quadratic is expressed as y = ax^2+bx+c. To convert the general equation to vertex form, we need to obtain this form:

(y- k)= a(x - h)^2

This could be done by using completing the square method.

</span><span>y = –3x^2 – 12x – 2
</span><span>y + 2 = –3(x^2 + 4x) 
</span>y + 2 -12 <span>= –3(x^2 + 4x + 4) 
</span>y - 10 = -3(x+2)^2

Therefore, the answer is the first option.
3 0
3 years ago
Read 2 more answers
A bathtub is being filled with water. After 10 minutes, there are
Ber [7]

Answer:

Everyone in the kingdom of Egypt was under the control of the pharaoh and it was believed that the pharaoh must obey the wishes of the ________.

Priests

Citizens

No one

Gods

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
The solution set for -p2 − 11p = 0 is { }. (Separate the solutions with a comma.)
ikadub [295]

Answer:

0,-11

Step-by-step explanation:

-p^2 − 11p = 0

Factor out -p

-p( p+11) =0

Using the zero product property

-p =0    p+11 =0

p =0      p = -11

3 0
3 years ago
Two items in a package have a combined weight of 6 1/4 kg. If one weighs 2 5/8 kg what is the weight of the second item?
mamaluj [8]

Answer:

3 7/8

Step-by-step explanation:

6 1/4 = 25/4 and 2 5/8 = 19/8

25/4 - 19/8 = 3 7/8

6 0
3 years ago
3) Let h(x)= |2x|-4. Find h(x) when x = -7.<br> a) -10<br> b) 10<br> c) -13<br> d) 13
svlad2 [7]

Answer:

h(x) = 10

Step-by-step explanation:

Given

h(x) = |2x| - 4

x = -7

Find h(x)

Substitute -7 for x

h(x) = |2*-7| - 4

h(x) = |-14| - 4

Absolute values return positive. So:

h(x) = 14 - 4

h(x) = 10

8 0
2 years ago
Other questions:
  • T-12/2 = 3t/2 - 3<br><br> 1. -3<br> 2. -1<br> 3. 1<br> 4. 3
    5·1 answer
  • 4n-40=-14n+14 how do I solve this ?
    11·2 answers
  • Which equations will help you solve this problem? There are 18 muffins on a plate. If they are split equally among 9 people, how
    15·1 answer
  • What is DE? <br><br> AC= 12.6
    10·2 answers
  • What is C a-c=r-d ; C
    5·1 answer
  • What is the inverse of f(x)=1/17x-3​
    12·1 answer
  • Compare the line passing through the points (-2, 9) and (4, 6) to the line given by the equation y= 2/5 x -4.
    9·1 answer
  • Inspect the mathematical expression. 15 times 1/x - 3x
    10·1 answer
  • Please help
    6·1 answer
  • Find 5 Rational Numbers Between 1 and 2 using (a+b/2) where a=1 and b=2.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!