anonymous
  • anonymous
find the area of the region inside the lemniscate r^2 = 2(a^2)(cos2theta) a>0
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
The element of area for a lemniscate in polar coordinates is given by,\[dA=\frac{1}{2}[r(\theta)]^2d{\theta}\]For your case, the area will be given by,\[A=\int\limits_{{\theta}_1}^{{\theta}_2}\frac{1}{2}(2a^2\cos(2{\theta}))d{\theta}=\left[ \frac{a^2}{2}\sin(2{\theta}) \right]_{{\theta}_1}^{{\theta}_2}\]
anonymous
  • anonymous
what is the theta 1 theta 2?
anonymous
  • anonymous
Your limits - you're integrating from one angle to another.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
\[A=\frac{a^2}{2}\left( \sin(2{\theta}_2)-\sin(2{\theta}_1) \right)\]
anonymous
  • anonymous
i mean, what is the value of theta 1 and theta 2? I am confused on how to find the limits of integration.
anonymous
  • anonymous
You should be given some information in the question. Usually you're told the angles explicitly. Sometimes you may need to work them out from the geometry of the situation. If the question you've posted is complete, then there's nothing more you can do. This is the formula someone would then use to find a numerical value. Though, like I said, unless you're given the limits, or are asked to find them from other information, what's been posted is as far as you can go.
anonymous
  • anonymous
okay. Thank you very much :D
anonymous
  • anonymous
No probs.

Looking for something else?

Not the answer you are looking for? Search for more explanations.