1
vote
1answer
21 views

Double integral And polar coordinate system

I have to evaluate this integral over the domain D The Plot would be like this: I decided to use polar coordinate system using it It gives me this but I don't know the upper limit of ...
0
votes
1answer
300 views

Area that lies inside both curves: $r=sin2\theta, r=cos2\theta$

My integral is setup as: $$A=8\int_0^\frac{\pi}8{\frac12sin^22\theta}\space d\theta - 8\int_{\frac{\pi}8}^0{\frac12cos^2 2\theta}\space d\theta$$ $$=8\int_0^\frac{\pi}8{\frac12sin^22\theta}\space ...
0
votes
1answer
51 views

confusing intergration

given $$r=4e^{3\theta} \space \space \space \space dr/d\theta=(3*4*e^{3\theta})$$ $$l=\int \sqrt(4e^{3\theta})^{2}+(3*4*e^{3\theta})^{2} \rightarrow $$ why does the integral $$ ...
1
vote
2answers
236 views

Evaluating the area in the polar coordinates

So the problem asked me to find the area of the region that lies inside both of the circles $$r=2sin\theta, \quad r=sin\theta +cos\theta $$ I know that $r=2sin\theta$ is $x^2+(y-1)^2=1,$but ...
2
votes
3answers
97 views

Finding a length of arc, what's wrong?

Find: $$ \int \sqrt{x^{2}+y^{2}}dl$$ $$L: x^{2}+y^{2}= Rx$$ (at image $p' = -R\cdot \sin(\phi)$ )
3
votes
3answers
747 views

Why is the formula for the area of a cardioid $ \int_a^b \frac{1}{2} r^2 d \theta$

I've seen this expression in many places :$\int_a^b \frac{1}{2} r^2 d \theta$ and was wondering if someone can explain where this came from? I've noticed that it's sometimes explained in conjunction ...
1
vote
1answer
436 views

Find the area of the shaded region between $r=e^{\theta/2}$ and $r=θ$ .

That's the picture of the shaded region I have to find the area of. I'm totally stuck on this problem mainly because these two curves don't intersect so I'm not sure how to find the bounds of ...
1
vote
2answers
290 views

Changing Variables in double integral

I have these particular exercise that i cannot solve. I know i have to change the variables, but i cannot figure out if i should use polar coords or any other change. Let D be the region delimited ...
0
votes
2answers
194 views

Length of a plane curve in polar coordinate

Consider the plane curve $\gamma$ in polar coordinates: $$ r=r_0+e^{\lambda\theta}, \quad \theta_1 \le \theta \le \theta_2, $$ where $r_0,\lambda,\theta_1>0$. Is it possible to compute explicitly ...
0
votes
1answer
1k views

Question about the limits of integration using polar coordinates

I haven't been able to find an answer to something I've been thinking about. If you are taking the integral of a circle in polar coordinates you always use the limits for theta as $0$ to $2\pi$. ...