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3 years ago

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

1 answer:

5 0

Let 9x^2-1 = y^2
=> 18xdx = 2ydy 
=> ydy = 9xdx 

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

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

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

y=tanz 
dy = sec^2z dz 

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

=81/4*(pi/3-pi/4) + 81/4*(sin(2pi/3)-sin(pi/2)) + 81/8 * (pi/3-pi/4) 
+ 81/32 *(sin(-pi/3)-sin(pi)) 
=81(pi/48+pi/96+1/4*(sqrt(3)/2 - 1) - 1/32 * sqrt(3)/2) 
=81/32*(pi+3sqrt(3)-8)

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Read 2 more answers

Combine like terms. x^2y-3xy^2-6x^2y

balu736 [363]

The result after combining like terms is: $-5x^2y-3xy^2$

Step-by-step explanation:

Given expression is:

$x^2y-3xy^2-6x^2y$

The like terms are those terms with whom the variable or product of variables is same.

As in the given expression, first and third, both terms have x^2y so both terms are like terms

Combining like terms, means the indicated operation is performed on them

So,

Combining like terms:

$x^2y-6x^2y-3xy^2\\= -5x^2y-3xy^2$

Hence,

The result after combining like terms is: $-5x^2y-3xy^2$

Keywords: Expressions, polynomials

Learn more about polynomials at:

#LearnwithBrainly

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2 years ago

Suppose your car has hhh liters of engine oil in the morning. During the day, some oil may have leaked, you may have added more

Igoryamba

Answer:

g = (h+a) - l

None of them

Step-by-step explanation:

Suppose your car has h liters of engine oil in the morning. During the day, some oil may have leaked, you may have added more oil, or both. The oil level in the evening is g liters. Which of the following expressions always represents how far away the new oil level is from the previous oil level? H+G lGl none of them

Let

h = liters of oil in the morning

l= liters that has leaked

a= liters that were added during the day

g= amount of liters at the end of the evening

Total liters of oil in the evening= (litres of oil in the morning + litres of oil added during the day) - litres of oil that leaked

Substituting each variable into the formula, we have

g = (h+a) - l

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3 years ago

The relationship between the number of gallons of water in a tank and number of hours is proportional. One point on the line mod

Over [174]

Answer:

Step-by-step explanation:

I am assuming the tank starts empty. It means that in 1 hour the tank has half that water, or 3600 gallons. And the good thing of lines passing through 0.0 is that the value at 1 IS the slope we need. ie 3600.

At this point it's easy to find that if in 2 hours it filled 1/10th of the tank, in 20 hours the tank will be full.

Graph done with paint, obviously not to scale.

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2 years ago

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

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