All Questions
Tagged with bounds-of-integration polar-coordinates
8
questions
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how to write this region $D$ in relation to $r,\theta$ in this $\iint_Df(x,y)dxdy$ where $D=\{x^2+y^2 \le1,x+y\le 1\}$ and $D=\{x^2+y^2\le1,x+y\ge1\}$
I have attached two photos showing the integration bounds and I find it tricky how to express $r$ and $\theta$ in those two, if $x=r \cos{\theta}$ and $y=r\sin{\theta}$, so any help is very much ...
3
votes
1
answer
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How do I find the bounds of this particular integral?
I want to convert this integral to Polar Coordinates to solve it: $\int_{0}^{2}\int_{0}^{\sqrt{y}}4xy^{2} \, dx \, dy$
What would be the bounds of $r$ and $\theta$ be?
I know how to solve the integral ...
1
vote
1
answer
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Evaluation of $~\iint_{D} {x^2-y^2 \over 1+x^4+y^4 } \mathrm{d}x \mathrm{d}y~$ where $~D~$is of bounded and closed and line symmetric with $~y=x$
$~D:=$domain where it is bounded and closed in $~ \mathbb R^2 ~$ and line symmetric with $~ y=x ~$
$$
I:=\underbrace{\iint_{D} {x^2-y^2 \over 1+x^4+y^4 } \mathrm{d}x \mathrm{d}y}_{\text{I want to ...
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1
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Determining Bounds of Theta for Double Integration of a Polar Region
Given the region $$ R:(x, y | x^2 + y^2 \le 4x) $$ And given the function $f(x, y) = \frac{x}{\sqrt{x^2+y^2}}$, find the double integral of the polar region.
So upon sketching the graph we get a ...
- 11
0
votes
1
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Compute Triple integral for each "R" > 0
Compute for each $R >0$ the following:
$$
\int\int\int (x^2 + y^2+z) dV\;\text{ over the region: }\;x^2 + y^2+z^2 ≤ 2Rz
$$
I decided to use polar:
Starting with $R=1$
rearranging the region I ...
0
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1
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60
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calculating the area in polar coördinates
I have difficulties calculating the area and setting the right boundaries of the following polar coördinates:
$$r=2(1+cos(\theta) ) $$
Thanks in advance
- 109
1
vote
1
answer
341
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polar coordinates for integral bounds with parallelogram as region
I'm having trouble with this problem: Evaluate the following double integral
$$
\iint_D (x^2+y^2) \,\text d x\,\text dy
$$
where $D$ is the region comprised of a parallelogram with the corners $(0,0)...
- 399
2
votes
3
answers
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Evaluating $\int_{-\infty}^\infty 1-e^{-\frac{1}{x^2}}{\rm d}x$
I am interested in the improper integral: $$I=\int_{-\infty}^\infty 1-e^{-\frac{1}{x^2}}{\rm d}x=2\int_{0}^\infty 1-e^{-\frac{1}{x^2}}{\rm d}x$$ which I am fairly sure converges.
I broke the integral ...
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