TylerD
  • TylerD
@ganeshie8
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!
TylerD
  • TylerD
think my teacher might be wrong on something, need to check here. https://www.desmos.com/calculator/mdavtmnba2 for that graph, find the area inside the rose, but outside the circle.
TylerD
  • TylerD
teachers solutions say just integrate (4cos(2theta))^2-2^2 from 0 to pi/6 then use symmetry.
TylerD
  • TylerD
teacher used this equation here http://tutorial.math.lamar.edu/Classes/CalcII/PolarArea_files/eq0008MP.gif but im not sure if u can do that in this case?

Looking for something else?

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

More answers

TylerD
  • TylerD
|dw:1438082191447:dw|
ganeshie8
  • ganeshie8
You want to find that area and multiply by 8 is it
TylerD
  • TylerD
ya
TylerD
  • TylerD
|dw:1438082672639:dw| but wouldnt that integral cut off there
ganeshie8
  • ganeshie8
Oh you're right, my bad, lets try again
ganeshie8
  • ganeshie8
\(\large \int\limits_{0}^{\pi/4}\frac{1}{2}(4\cos2\theta)^2~d\theta\) gives below shaded area |dw:1438082959464:dw|
ganeshie8
  • ganeshie8
\(\large \int\limits_{0}^{\pi/6}\frac{1}{2}(2)^2~d\theta\) gives below shaded area |dw:1438083157606:dw|
TylerD
  • TylerD
next one would be pi/6 to pi/4 for the cos(2theta)
ganeshie8
  • ganeshie8
\(\large \int\limits_{\pi/6}^{\pi/4}\frac{1}{2}(4\cos2\theta)^2~d\theta\) gives below shaded area |dw:1438083357364:dw|
ganeshie8
  • ganeshie8
does that look okay now ? :)
TylerD
  • TylerD
yep.
ganeshie8
  • ganeshie8
lets work this and see if it matches with your teacher's answer
ganeshie8
  • ganeshie8
just want you notice that we're adding and subtracting that last orange piece, which is simply a waste of work... evaluate the integrals and you will see what i mean
ganeshie8
  • ganeshie8
your method : http://www.wolframalpha.com/input/?i=%28%5Cint%5Climits_0%5E%7B%5Cpi%2F4%7D+1%2F2%284%5Ccos%282%5Ctheta%29%29%5E2+d%5Ctheta%29+-+%28+%5Cint%5Climits_0%5E%7B%5Cpi%2F6%7D+1%2F2*%282%29%5E2+d%5Ctheta%29+-+%28%5Cint%5Climits_%7Bpi%2F6%7D%5E%7B%5Cpi%2F4%7D+1%2F2%284%5Ccos%282%5Ctheta%29%29%5E2+d%5Ctheta%29 your teacher's method : http://www.wolframalpha.com/input/?i=%28%5Cint%5Climits_0%5E%7B%5Cpi%2F6%7D+1%2F2%284%5Ccos%282%5Ctheta%29%29%5E2+d%5Ctheta%29+-+%28+%5Cint%5Climits_0%5E%7B%5Cpi%2F6%7D+1%2F2*%282%29%5E2+d%5Ctheta%29
ganeshie8
  • ganeshie8
\(\large \int\limits_{0}^{\pi/\color{red}{6}}\frac{1}{2}(4\cos2\theta)^2~d\theta\) gives below shaded area |dw:1438084278198:dw|
TylerD
  • TylerD
dang, was hoping to get extra credit for proving it wrong.
ganeshie8
  • ganeshie8
Haha! you had the right idea, pretty sure you will find other opportunities to catch ur teacher's mistakes ;)

Looking for something else?

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