Integrate 1/((x^5)*sqrt(9*x^2-1)) ...?
1 answer:
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>
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Answer:
0 is the answer same as 0+0=0
hope this helps
have a good day :
Step-by-step explanation:
-3(x - 3) > 5 - 5x
use the distributive property
-3x + 9 > 5 - 5x
subtract 5 from both sides
-3x + 4 > -5x
add -3x to both sides
4 > -2x
divide both sides by -2 to isolate x
x > -2
The correct answer is D. x > -2.
Answer: b is the answer
Step-by-step explanation:
i need a graph so i can see then i will solve it
Answer:
dimensions = 10.8 X 4
Step-by-step explanation:
Breadth/ width of room = x
Length of room = 6.8 + x
perimeter = 2 ( L + B )
29.6 = 2 ( 6.8 + x + x )
29.6/2 = 6.8 + 2x
14.8 - 6.8 = 2x
8 = 2x
8/2=x
4=x
Length of room = 6.8 + x = 6.8 + 4 = 10.8 m
Breadth/ width of room = x = 4m