ok, I am a bit confused here. Do u mean sub those parametric equations into y=y(x) or y(1+y`2)=C?
if its y=y(x), that's how i got 1-cost=1-cost(t-sint).
If its the latter, then dy/dx=sint/(1-cost).
then i plug it into the equation to get 1-cost(1+(\frac{sint}{1-cost})2)=C
->...
if i sub those in, i get 1-cost=1-cos(t-sint). I am stuck here :(
As for questions number 2, i got to x=\int\frac{2cu^{2}}{(1+u^{2})^{2}}du. where do i go from here?
(with u^2 = y/(c-y) )
1. use the parametric equations of a cycloid ( x=a(t-sint), and y=a(1-cost) ) to show that y=y(x) is the solution of the differential equation for any parameter a. Find the relationship between the radius a in the parametric equations and the constant C in y(1+y`2)=C.
2. Solve the equation...
O, I am sorry. I did my math incorrectly...
after reworking the problem, using integration by parts,
i'm stuck at
(-t^(1/2))/(e^t)|[tex]^{infinity}_{0}tex]+(1/2) (original integral except t^-1/2)
after further integration, isn't it an endless cycle?
okay, if i numerically approximate by plugging in 3/2 into the gamma function, i get infinity.
how am i supposed to use that information to arrive at the conclusion in #2?
1. Numerically approximate \Gamma(\frac{3}{2}). Is it reasonable to define these as (\frac{1}{2})!?
2. Show in the sense of question 1. that (\frac{1}{2})! = \frac{1}{2}\sqrt{\pi} at least numerically.
How am i supposed to attempt this numerically? given that i do not know additional...
So I am guessing that \int^{\infty}_{o}\frac{sinx}{x} converges to pi/2?. The question seems straight forward but my teacher isn't that forgiving, I am thknking there's more to it?
1. Let F(x)= \int^{x}_{0} \frac{sint}{t} and f(x) = \frac{sinx}{x}. If x approaches infinity, F(x) approaches \pi/2. So, Explain what does this mean for the improper integral \int^{\infty}_{o}\frac{sinx}{x}
Homework Equations
Explain what does this mean for the improper integral...
1. Evaluate exactly (in terms of \pi) the definite integral \int^{\pi/2}_{-\-\pi/2} \frac{dx}{sinx + 2cosx +3}
Homework Equations
How do i do this? Step by step instructions if possible.
The Attempt at a Solution
I've tried to manipulate the integral but still don't get anything. I...