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Countable vs uncountable infinitesimals in calculus
There is a general understanding that some infinities are bigger than others, in particular the infinity of the integers, the countable set of infinite discrete elements, and that larger infinity of ...
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Area of a region bounded by a circle and vertical line using integration
What is the area of the right region bounded by $x^2 + y^2 =25$ and $x = -3$?
My attempt solution: I solved first for the area of the left region and subtracted it from the area of the circle, which ...
- 73
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Area of a Region Bounded by a Circle and Vertical Line
What is the area of the right region bounded by $x^2 + y^2 =25$ and $x = -3$?
My attempt solution: I solved first for the area of the left region and subtracted it from the area of the circle, which ...
- 73
1
vote
1
answer
375
views
How to evaluate Area of $B:= \{(x,y,z) \in A | z \le 1 \}$ with $A:=\{(x,y,z) \in \mathbb{R}^3 | x^2 + y^2 = z\} = \frac{\pi}{6}(5 \sqrt{5}-1) $?
I have following problem:
Let $$A:=\{(x,y,z) \in \mathbb{R}^3 | x^2 + y^2 = z\} \\
B:= \{(x,y,z) \in A | z \le 1 \}. $$
Compute the area $\mu_2(B) $.
First, I thought $\mu_2(B) $ would just be the ...
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