ok, so integral dx/[(x2 - 2x + 2))2] = integral dx/[((x-1)2 + 1)2]
t = x-1; dt = dx
integral dt/(t2 + 1)2
t = tan(u); dt = sec2(u)du
= integral sec2(u)du/(tan2(u) + 1)2
= integral sec2(u)du/(sec2(u))2 = integral du/sec2(u)
= integral cos2(u)du = 1/2 integral (1 + cos(2u))du
= (1/2)u +...
Homework Statement
Integral of dx/[(x2 - 2x + 2)2]Homework Equations
Trig substitution rules:
for expression sqrt(a2 - x2)
make x = asin(t) with -(pi/2) < t < (pi/2)
for sqrt(x2 - a2)
make x = asec(t) with 0< t < (pi/2)
and
for sqrt(a2 + x2)
make x = atan(t) with -(pi/2) < t < (pi/2)The...
but according to integration by parts, 1/sqrt(4+r^2) must be dv not v, if you make u = x^3. Also I did not follow how you got the sinh^{-1}(r/2) if the denominator is (a2 + u2)1/2 not (a2 - u2)1/2
I see what you did for the most part, except that last issue I mentioned. Thnx.
Homework Statement
The definite integral of from 0 to 1 of ∫ (r3)dr/sqrt(4+r2)Homework Equations
∫udv = uv - ∫vdu
∫du/sqrt(a2 - u2) = arcsin(u/a) + C
∫du/(asqrt(a2 - u2)) = (1/a)arcsec(u/a) + C
The Attempt at a Solution
I made u = (4+r2)-1/2
because I thought it easier to get it's...
Oh!
If I put x=e, then I get g(e) = 2. So (e,2). Then it's inverse is (2,e) which matches with g-1(2) to give me e. I see how that could work, but how did you have the intuition to add e to the original problem? I suppose it's a matter of plugging something that seems like it would give...
The answer choices are: A) 1 B) 2 C) e D) e2 E) 0
One of these is the correct "evaluation".
I follow that if f(x) =y then f-1 (y) = x
But when I don't know how to get to x, I'm not going to be able to solve this.
Homework Statement
The function g(x) = (x2/e) + 2 ln(x) - e on (0,infinity) is one-to-one. Evaluate g-1(2)Homework Equations
Find x in terms of y. Then switch x and y. Plug in 2 to the new equation.The Attempt at a Solution
I can think of no way to get x explicitly in terms of y. I...
oh! Duh. I can combine the other two resistors into one and compare it as a two wire problem. Too bad it's not intuitive enough as to just add and multiply things, since I need to find the inverse sum of the two resistors first. Thnx.
Homework Statement
Say I have a circuit that splits into three parallel wires. They each have a resistors on them of 2, 3, and 4 ohms respectively. They reconnect and their final current is 10 Amps. Is there a more intuitive way to find the current on each wire based on the ratios of ohms...
Homework Statement
If theta is the angle between two non-zero vectors A and B, then which of the following angles theta results in A dot B = |A x B|?
Homework Equations
A dot B = ABcos(theta)
A x B = ABsin(theta)
The Attempt at a Solution
There were two choices in the multiple choice answers...
So the only way to solve this is to know the actual values of Earth's mass and Radius and adjust to their respective ratios and plug in the m? I was hoping there would be a way to simply utilize the ratios without having to know the Earth's mass or Radius. Also, I understand that my answer is...
Homework Statement
The mass of a hypothetical planet is 1/100 that of Earth and its radius is 1/4 that of Earth. If a person weight 600 N on Earth, what would he weigh on this planetHomework Equations
F = (G x M x m)/(R2)The Attempt at a Solution
Well I know the mass of the person is the same...
What you said doesn't completely agree with the information, because the mass of the horizontal rod is different from the mass of the vertical rod. Also, where are you getting the mass of the rod with m = 2*(m*L/2)? Your explanation confuses me. I'm thinking that the mass is relative to the...