Graphing Polar Coordinates: 0 ≤ θ ≤ π and 0 ≤ r ≤ 4

Fatima Hasan
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Homework Statement


Graph the set of points whose polar coordinates satisfy the given equation or inequality.

0 ≤ θ ≤
f1q8g1.jpg
, 0 ≤ r ≤ 4

Homework Equations


-

The Attempt at a Solution


image.png

Is it correct ?
 

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Homework Statement



Graph the set of points whose polar coordinates satisfy the given equation or inequality.
0 ≤ θ ≤ π, r ≤ 3

Homework Equations


-

The Attempt at a Solution


image.png

Could someone check my answer ?
 

Attachments

  • image.png
    image.png
    7.8 KB · Views: 634
Both correct.
I merged the two threads as the questions are so similar.
 
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Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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