Could someone help me with these two problems? I've been at them for an hour, but have very little clue how to go about solving either of them.
Homework Statement
1)∫ 6 csc^3 (x) cot x dx
Homework Equations
The Attempt at a Solution
6 ∫ csc^3 (x) dx) / tan x
csc^3 / tan x =...
Here is the work that i have done so far, corrected for the mistake that you pointed out earlier.
1) Find the length of the curve. y = x^3/6 + 1/(2x) from x = 1 to x = 4
L = ∫sqrt(1 + (d(x^3/6 + 1/(2x)/dx))^2) dx from x = 1 to 4
(d(x^3/6 + 1/(2x)/dx) = (x^3/6 + 1/(2x)
((x^3/6 +...
Now how would I go about factoring the expression that I get when I correct my mistakes? What I have now is
∫sqrt(x^6/36 + x^2/6 + 1/(4x^2) + 1) dx from x = 1 to 4
Here is the work that i have done so far:
1) Find the length of the curve. y = x^3/6 + 1/(2x) from x = 1 to x = 4
L = ∫sqrt(1 + (d(x^3/6 + 1/(2x)/dx))^2) dx from x = 1 to 4
L = ∫sqrt(1 + (x^2/2-1/(2 x^2))^2) dx from x = 1 to 4
L = ∫sqrt(1 + x^4/4 + 1/(x^4) - 1/2) dx from x = 1 to 4
L...
∫sqrt(x^4/4 + 1/(x^4) + 1/2) dx from x = 1 to 4
Could someone help me solve this? I can't seem to find a substitution that works, or find the square root of (x^4/4 + 1/(x^4). Any help would be very appreciated.
Thanks in advance!