Homework Statement
I'm having major issues working out how to integrate
\int\frac{1}{F-Gx+x^{2}}dx , where F and G are constants.
Homework Equations
The Attempt at a Solution
Maple tells me it is an inverse hyperbolic tangent of some description, and I know I have to...
Homework Statement
Im getting very confused with working out how to integrate the following double integral with an absolute value:
\int^{2}_{-2}\int^{2}_{-2}\left|x^{2}+y^{2}-1\right|dxdy
Homework Equations
The Attempt at a Solution
I know you have to split it down into where it...
Homework Statement
I am getting very confused as to how to solve this question about determining acceleration in polar coordinates.
First I am asked to determine the relation between the cartesian velocity (v_x , v_y) and the polar velocity (v_r , v_b) , where r is the radius and a is the...
Ah that´s great thanks. So that proves it for when (x,y) are in B.
But when (x,y) are not in B, then we are integrating the function 0 on the interval R=[0,1]x[0,1] with limits of integration 0,1 and x,1 as above, which is 0...
Which is evidently not between 1/6 and 1/2...
So it is only...
Homework Statement
Prove the following inequality:
\frac{1}{6}\leq\int_{R}\frac{1}{y^{2}+x+1}\chi_{B}(x,y)dxdy\leq\frac{1}{2}
where B={(x,y)|0\leq (x)\leq (y)\leq1} and R=[0,1]x[0,1]
EDIT: The B region should be 0 less than or equal to x less than or equal to y less than or equal to 1...