# Some tricky diff problems

• May 8th 2008, 03:29 PM
dankelly07
Some tricky diff problems
Hi I have a some problems I could use help working through, if anyone could help me out here Id be v greatful!!

(1)

$\displaystyle \int {\frac{{dx}} {{\sqrt {4x^2 - 9} }}}$
(hyperbolic function)

(2)

$\displaystyle \oint\limits_r {\{ (x^2 - y)dx + (y^2 + x)dy\} }$

Where r is the closed path, mapped counterclockwise, described by the square with verticies at (0,0),(1,0),(1,1),(0,1)

(3)

- use greens theorem to evaluate

$\displaystyle \oint\limits_r {\{ (y\exp [x^2 y^2 ] - y)dx + (x\exp [x^2 y^2 ] + x)dy\} }$

where r, mapped counterclockwise, is the circle of th radius a with centre at the origin.
• May 8th 2008, 04:55 PM
o_O
$\displaystyle \int \frac{dx}{\sqrt{4x^{2} - 9}}$

Recall that: $\displaystyle \int \frac{dx}{\sqrt{x^{2} - a^{2}}} = \cosh^{-1} \left(\frac{x}{a}\right) + C$

So you have to factor out the 4 under the radical in the denominator so you can isolate it from the $\displaystyle x^{2}$ in order to use the standard integral.
• May 8th 2008, 06:48 PM
sleepingcat
For (2), can't you sum the integrals along each side of the square, since on any given side, either x or y is constant?
• May 8th 2008, 07:15 PM
topsquark
Quote:

Originally Posted by sleepingcat
For (2), can't you sum the integrals along each side of the square, since on any given side, either x or y is constant?

Yes.

-Dan