Finding Boundaries of a Definition Area

[Wi_N]

Homework Statement

Problem is part of a double integral. but my boundries are:

1<=x^2 + y^2 <=9 so between 2 circles with r1=1 and r2=3

and x<=y and y<=sqrt(3x)

the first boundry is obviously pi/4 and/or 3pi/4

the answer is pi/3 and i have no idea how u get that.

u obviously have to switch to polar coordinates but x=rcost y=rsint have no resulted in anything.

 

[Mark44]

Homework Statement

Problem is part of a double integral. but my boundries are:

1<=x^2 + y^2 <=9 so between 2 circles with r1=1 and r2=3

and x<=y and y<=sqrt(3x)

the first boundry is obviously pi/4 and/or 3pi/4

If you mean $\theta = \frac \pi 4$, then yes, that is a boundary, but $\theta = \frac {3\pi} 4$ isn't a boundary.

the answer is pi/3 and i have no idea how u get that.

Nor do we, since you haven't told us what you're integrating or shown how you got your result.

u obviously have to switch to polar coordinates but x=rcost y=rsint have no resulted in anything.

Are you assuming that the line boundary and the quadratic boundary intersect on the outer circle?

 

[LCKurtz]

Homework Statement

Problem is part of a double integral. but my boundries are:

1<=x^2 + y^2 <=9 so between 2 circles with r1=1 and r2=3

and x<=y and y<=sqrt(3x)

the first boundry is obviously pi/4 and/or 3pi/4

the answer is pi/3 and i have no idea how u get that.

Have you drawn a picture including $y =\sqrt 3 x$? What is its slope? Angle of inclination? That will tell you how to get $\theta$ for it.

 

[Mark44]

y<=sqrt(3x)

Have you drawn a picture including $y =\sqrt 3 x$?

Per the OP, it is $y \le \sqrt{3x}$, not $y \le \sqrt 3x$.

 

[LCKurtz]

Per the OP, it is $y \le \sqrt{3x}$, not $y \le \sqrt 3x$.

I'm guessing that the OP mistyped the problem, especially in light of what he says the answer is supposed to be.

 

[Mark44]

I'm guessing that the OP mistyped the problem, especially in light of what he says the answer is supposed to be.

Certainly within the realm of possibility.

 

[Wi_N]

you guys are right. thnks.