- #1
kandelabr
- 113
- 0
Homework Statement
i want to derive a formula for an ellipse sector. ellipse is not rotated and its center is in the origin. its semimajor and semiminor axis are a and b, respectively, and angle of the sector begins with t1 and ends with t2.
it's just a simple surface integral in polar coordinates, i did that already and got the result.
but then i found this:
http://mathforum.org/library/drmath/view/53635.html"
i also have noticed that at t1 = 0 and t2 = 2pi, the area calculated from that formula does not match A = pi*a*b.
there is a correction for the answer given by doctor sam just below the next post, but i have no clue where did that dTheta come from, i can't see a reason why a normal integration wouldn't give correct results.
what did i miss?
for calculating the area of the whole ellipse, we used the following transformation at lessons:
x = a r cos(fi)
y = b r sin(fi)
J (jacobi determinant) = abr
this thing works only for 0 < fi < 2*pi.
why?
why none of our professors mentioned any of these problems?
Last edited by a moderator: