Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
use parametric equations of the semi ellipse to find the area that it encloses.
x=2cos(t), y=3sin(t), t=[0,pi]
 one year ago
 one year ago
use parametric equations of the semi ellipse to find the area that it encloses. x=2cos(t), y=3sin(t), t=[0,pi]
 one year ago
 one year ago

This Question is Closed

mark_o.Best ResponseYou've already chosen the best response.1
\[\frac{ x ^{2} }{ 2^{2} }+\frac{ y ^{2} }{ 3^{2} }=1\] solving for y \[y=\sqrt{3^{2}(1\frac{ x ^{2} }{ 2^{2} })}\]
 one year ago

mark_o.Best ResponseYou've already chosen the best response.1
\[y=3\sqrt{(1\frac{ x ^{2} }{ 4 })}\]
 one year ago

mark_o.Best ResponseYou've already chosen the best response.1
1/2 area of semi ellipse A= \[=\int\limits_{0}^{2}3\sqrt{(1\frac{ x ^{?} }{ 4 })} dx\] substitute sin t=x/2, then dx=2 cos t dt, also t= [0,pi/2] 1/2 A=\[\int\limits_{0}^{\frac{ \pi }{ 2 }}3\sqrt{(1\sin ^{2}t)}(2\cos t dt)\] =\[\int\limits_{0}^{\frac{ 0 }{ 2 }}6\cos ^{2}tdt\] but cos^2 t=(1+cos 2t)/2 \[=6\int\limits_{0}^{\pi/2}\frac{ (1+\cos 2t) }{ 2 }dt\] =\[\frac{ 6 }{ 2 }\left[ t+\frac{ \sin 2t }{ 2 } \right]from 0 \to \frac{ \pi }{ 2 }\] \[\frac{ 1 }{ 2 }A=3\left[ \frac{ \pi }{ 2 }+0(0+0) \right]\] \[A=3\pi. \]
 one year ago

nublanthefabBest ResponseYou've already chosen the best response.0
thank you so much @mark_o.
 one year ago

mark_o.Best ResponseYou've already chosen the best response.1
YW good luck now :D ........ have fun solving :D
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.