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>
Answer:
Step-by-step explanation:
2. expand the brackets
3. take away the smallest x value to simplify 8x-5x=3x
4. 3x=-15 divide both sides by 3 to find the value of x
5. -15/3=-5 therefore x=-5
Good evening Gloria
3t(t+2)-3t² for t=19
Well the first thing we need to do is to replace 19 everywhere we see T
So let's do it together
3(19)(19+2)-3(19)²
57(21)-3(361)
1197-1083
= 114
I hope that's help and if you have questions please let me know :)
Please give my answer a Thanks and stars ↓
The answer would be the third option , because
Answer: c
Step-by-step explanation:
