Question

Sketch the indicated and integrate f(x,y) over D using polar coordinates. f(x,y)=2xy
x>=0 , y>=0, x^2+y^2<=49

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Answer 1

I got 7, where did i go wrong???

Answer 2

Dabears :D After I grab a shower I'll help you :P Give me 10 :P

Answer 3

yay! thanks malevolence :)

Answer 4

x^2 +y^2 <=49 will give you in polar coordinates:
r<=7
right?

Answer 5

\[x=r*\cos \alpha\]
\[y=r*\sin \alpha\]
integrate

Answer 6

yes thats why I was thinking 7ish?

Answer 7

\[=\int\limits_{0}^{\pi/2}\int\limits_{0}^{7}2*r ^{2}*\sin \alpha *\cos \alpha drd \alpha\]
seems like this should be right for x>=0 & y>=0

Answer 8

ohhh i think i see what i did

Answer 9

which gives me:
\[343/3 \int\limits_{0}^{\pi/2} \sin2\alpha d \alpha=343/3 (-\cos2\alpha)/2=343/3\]

Answer 10

how we doing? does it match the answer?

Answer 11

let me plug it in real quick

Answer 12

said it was wrong :(

Answer 13

shoot....
let me think

Answer 14

maybe for the polar coordinates ? f(x,y) = 2xy = 2(rcos (theta)(r sin theta) = r^2 sin 2 theta

Answer 15

I did the same thing...exactly

Answer 16

how did you get the cos for the integral above? I used same intervals but had (r^2sin2theta) no cos()

Answer 17

(r^2sin2theta)r dr dtheta -- i mean

Answer 18

you have the same... actually
x=rcos 7 y=rsin
so, F=2r^2 sin * cos = r^2 sin2 theta

Answer 19

\[\int\limits_{}^{}\sin2\beta d \beta=-1/2 \cos2\beta\]
right?

Answer 20

oh yeah, whooops :)

Answer 21

i do not see any mistakes...
I keep getting 343/3 as an answer...

I have a special software! - let me check!

Answer 22

okay thanks !

Answer 23

Well you have:
\[\int\limits_{0}^{\frac{\pi}{2}} \int\limits_{0}^{7}2r^2\sin(\theta)\cos(\theta)r dr d \theta\]
So that gives r^3.
Which makes the integrand
r^3sin(2theta)

Answer 24

Integrating r you get (1/4)r^4sin(2theta) Or:
(2401/4)sin(2theta)
Then integrating theta you get:
(2401/4)(-1/2)cos(2theta)
Evaluating:
(-2401/8)(-1-1)=2401/4?

Answer 25

Which is what wolfram gives me.

Answer 26

if this wasn't the internet, I'd shake your hand! thank you it was right

Answer 27

I forgot that pesky r on the outside!!

Answer 28

I even wrote it above haha

Answer 29

:D I'm glad. Mathematica also confirms this :P (wolfram but with straight input code)

Answer 30

perfect thanks again! and thx inik for helping me too!

Answer 31

I missed r^4.... ! shame :(