# Tagged Questions

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### Solving integral by going to polar coordinates [on hold]

Solve by going to polar coordinate system: $$\int_{0}^{5}dx \int_{0}^{\sqrt{25-{x}^{2}}} ln (1+{x}^{2}+{y}^{2})dy$$ How can i solve this? Can you write solving? !Sorry for mess and another language, ...
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 $$... 1answer 168 views ### Double integral convert in polar coordinates [closed] Calculate the double integral by transferring to polar coordinates:$$ I = \int_0^{5} \int_{0}^{\sqrt{\vphantom{\huge a}25 - x^{2}\,}} \ln\left(1 + x^{2} + y^{2}\right)\;{\rm d}y\,{\rm d}x $$Make a ... 2answers 177 views ### Evaluating the area in the polar coordinates So the problem asked me to find the area of the region that lies inside both of the circles$$r=2sin\theta, \quad r=sin\theta +cos\theta $$I know that r=2sin\theta is x^2+(y-1)^2=1,but ... 3answers 92 views ### Finding a length of arc, what's wrong? Find:$$ \int \sqrt{x^{2}+y^{2}}dlL: x^{2}+y^{2}= Rx$$(at image p' = -R\cdot \sin(\phi) ) 3answers 382 views ### Why is the formula for the area of a cardioid  \int_a^b \frac{1}{2} r^2 d \theta I've seen this expression in many places :\int_a^b \frac{1}{2} r^2 d \theta and was wondering if someone can explain where this came from? I've noticed that it's sometimes explained in conjunction ... 1answer 342 views ### Find the area of the shaded region between r=e^{\theta/2} and r=θ . That's the picture of the shaded region I have to find the area of. I'm totally stuck on this problem mainly because these two curves don't intersect so I'm not sure how to find the bounds of ... 2answers 234 views ### Changing Variables in double integral I have these particular exercise that i cannot solve. I know i have to change the variables, but i cannot figure out if i should use polar coords or any other change. Let D be the region delimited ... 2answers 162 views ### Length of a plane curve in polar coordinate Consider the plane curve \gamma in polar coordinates:$$ 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 ...
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 $2\pi$. ...