Area Definition and 1000 Threads

Homework Statement Evaluate the definite integral for the surface area generated by revolving the curve about the y-axis: Homework Equations Curve: y=9-x^2 about y-axis The Attempt at a Solution Attached

I do not know how to formulate formulas on this forum so I just wrote it neatly on a piece of paper and linked it. http://puu.sh/8fwXr.jpg Thankss.

Here is the question: I have posted a link there to this thread so the OP can view my work.

Homework Statement Use Green’s Theorem to find the area of the region between the x – axis and one arch of the cycloid parameterized by p(t) = < t-2sin(t),2-2cos(t)> for 0≤t≤2∏ p Homework Equations The Attempt at a Solution My problem here is that I get different answers depending on if I...

Hi. I understand how to solve surface Area using integration when it is to be revolved about the x or y axis. But when the axis is not x or y I have a difficult time solving it. Please help me. Here is the equation sqrt(x+1) rotated at x=-1 and y=5. the bounds are 1 to 5. since y=sqrt(x+1)...

please tell me if i did this correctly: task: I'm trying to divide the differential dA by dV where.. dA = differential surface area of a sphere, dV = differential volume of a sphere dA=8\pirdr dV=4\pir2dr so then dA/dV= 2/r Also, if i treat this as a derivative, then would...

Problem: Let $\dfrac{1}{a_1-2i},\dfrac{1}{a_2-2i},\dfrac{1}{a_3-2i},\dfrac{1}{a_4-2i},\dfrac{1}{a_5-2i}, \dfrac{1}{a_6-2i},\dfrac{1}{a_7-2i},\dfrac{1}{a_8-2i}$ be the vertices of regular octagon. Find the area of octagon (where $a_j \in R$ for $j=1,2,3,4,5,6,7,8$ and $i=\sqrt{-1}$). Attempt...

Let's say that you have an open tank of water and a hose connected to the bottom of it. Water is flowing out of the hose. You then cover half of the hose with your thumb. Will the flow rate (liters/second) right before you cover the hole be the same, less, or greater than right after you cover...

Homework Statement hi,guys. The directions of shooting e=cos\alphacos\varphii+cos\alphasin\varphij+sin\alphak 0<\varphi<=2π;\varphi -horizontally \alpha[0,π];\alpha is vertically initial speed=v0 I need to calculate the surface equation of canon shots (where it hits). In other words equations...

Hi, I just need these solutions checked. Thank you in advance! Consider the region bounded by the following curves ##y=x-3, y=5-x, \text{and}\ y=3##: 1.) set up an integral expression that would give the area of the region of y as a function of x: ##y = x-3 = 5-x## ##x + x - 3 -...

How do I find the direction of area vector of a surface?

Homework Statement Problem in attachment. Homework Equations The Attempt at a Solution Unfortunately I was unable to attend my only class where my proffessor taught this method of solving area. Plus my prof and classmates won't help me. Does anybody know how to solve area...

Hi all! I am currently reading a review "Area law for the entanglement entropy" by Eisert, Cramer and Plenio (2010). From what I understand: 1. In one dimension, for local gapped models, we have an area law for entanglement entropy. 2. In one dimension, some models with long range...

Here is the question: I have posted a link there to this thread so the OP can view my work.

What does "cross section area" mean when dealing with stress/strain? Homework Statement For clarification, here is an example problem: A circular steel wire 2 m long must stretch no more than 0.25 cm when a tensile force of 400 N is applied to each end of the wire. What minimum diameter is...

Homework Statement Find the area of the region in the first quadrant, which is bounded by the x-axis, the line x = 2 and the circular arc x^2 + y^2 = 8Homework Equations The Attempt at a Solution I didn't use the hint given in the question but does my answer still makes sense. Did I set up the...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Hello, I'm new here, but I have some questions which i'd like to ask. I had this idea about corrugated wings to increase the wing surface area (thus increasing lift), but quickly realized that this would also increase the wings drag as it would have a larger cross section breaking through...

I can compute the area of the rectangle formed by Δx and Δy simply by product ΔxΔy. Now, how can I to compute the area in gray given Δr and Δθ? Also, I can to compute the volume of a parallelepiped formed by Δx, Δy and Δz, simply multiplicand ΔxΔyΔz. But, how can I compute the volume...

I would like to derive the surface area for an equation in the form of \(z = f(x, y)\). For example, if I have a sphere \((b^2 = x^2 + y^2)\), the surface area is circumference times arc length \((SA = 2\pi r\ell)\). Here I can take an arc and break it up into n parts to find the differential...

There is a graph associated to it. Please look at the screenshot. Ok, so, here is my process. I modeled the three functions. y=x y=1/a^2 x and y=1/x Then, I calculated A using calculus. (Integrals) Integral of x-1/a^2 x from 0 to 1 + integral of 1/x-1/a^2 x from 1 to a A=1-1/a^2...

See image attached. (I've had a google but can't find anything). I am trying to understand the expression : Rdθ.2∏Rsinθ Here are my thoughts so far: Rdθ is the width of a strip, θ being the variable changing/to integrate over, giving arise to the elements. 2∏Rsinθ must then...

I'd love it if someone could verify whether or not I did this problem correctly. A stained-glass window is a disc of radius 2 (graph r=2) with a rose inside (graph of r=2sin(2theta) ). The rose is red glass, and the rest is blue glass. Find the total area of the blue glass. So I set...

Decided to make a new thread so it wouldn't be jumbled up with the other thread I posted about this particular problem. Question: Find the area of the region which is inside both $$r = 2$$ and $$ r = 4sin(\theta)$$ So solving, I know that $$sin\theta = \frac{1}{2}$$. I also sketched a picture...

Homework Statement Suppose we have a circle of radius r, and two points A and B on the circle. We want to know the area of the sector cut off by A and B as a function of radius r and AB (the length of SEGMENT AB) Without calculus or trig. Homework Equations The Attempt at a...

I have been given various corners which are x and y coordinates for a shape. The coordinates are listed in a vector e.g. xpoints = [x1, x2, x3, …, xn, x1] and ypoints = [y1, y2, y3, …, yn, y1] so that corner 1 would be (x1,y2) and corner n would be (xn, yn). I have listed the first point last so...

Long story short, I'm taking my Intro Biology class/lab right now. My current plan is grad school in a field of Biology, so obviously I've been keeping an eye out for a field that might interest me. We are currently studying Plants and Animals, and I've become hooked on Marine Invertebrates...

Find the area of the region which is inside both$$ r = 2$$ and $$r = 4sin(\theta)$$How do I set up this? would I do.. $$\int ^{2\pi}_0 \frac{1}{2} [ r ] ^2 dr$$ ?

Hey so another expressing functions question: A rectangle has on corner on the graph of y=36-x^2, another at the origin, a 3rd on the positive y-axis, and the fourth on the positive x-axis. Express the area A of the rectangle as a function of x. What is the domain of A? For what value of x is...

I know this is relatively easy but I'm just confused on the process... Find the area inside one loop of a four leafed rose $$r = cos(2\theta)$$. I know that the formula is $$A = \int ^{\beta}_{\alpha} \frac{1}{2} [f(\theta)]^2$$ right? I'm just not sure what to plug in or solve for.

Here is the question: I have posted a link there to this thread so the OP can view my work.

Hi, I wondered whether a well known expression is known that computes the area between two vectors in R^n. By area between two vectors, I mean the area that would be computed by considering the subspace spanned by the two, projecting the entire space to a "parallel plane" and then finally given...

Calculate area D=(x,y): -1≤X≤0 0≤Y≤ X²+4x+5 I started with dA=f(x) dx ∫f(Y=x²+4x+5) [F(x) x^3/3 + 2X²+5X] higer limit 0 lower limit -1 F(0)=0 F(-1)=-3.5 F(a)-F(b) = -3,5 I don't get this ... ?? What am i missing? Regards!

Hey! I'm a complete newbie to integral calculus (and well, to math in general - but I'm trying to learn!) and I have a bit of a problem. I already get the feeling that the solution is ridiculously simple, but my brain just isn't making the connection. Homework Statement Given are two...

demonstrate or show that the figure area is = a/b sen alpha triangle a = triangle B maybe this is the main premise

I found this matrix in the wiki: https://fr.wikipedia.org/wiki/Vitesse_ar%C3%A9olaire#.C3.89valuation_en_coordonn.C3.A9es_cart.C3.A9siennes I think that it is very interesting because it express d²A not trivially as dxdy. So, I'd like of know if exist a matrix formulation for volume...

In wiki there is the follows formula: https://en.wikipedia.org/wiki/Green%27s_theorem#Area_Calculation But, I don't understand why M = x and L = -y. I don't found this step in anywhere.

Using calculus, how would I derive a formula for the exposed surface area of a ball floating in water? For such a formula to be a good candidate, it would have to consider oscillations of the water and placid water. The surface area of a sphere is \(A = 4\pi r^2\).

Hello, after searching around on the internet about this problem, it looks like it is Cramer's rule that I want to use, though it wasn't shown to us under that name. My textbook doesn't cover the material required for this problem, so i'd really like to run what I have done past you guys...

Hello, I am looking for the area between \[f(x)=x\cdot ln^{2}(x)-x\] and the x-axis. I have a solution in hand, it suggests that the area is: \[\int_{\frac{1}{e}}^{e}(x-x\cdot ln^{2}(x))dx\approx 1.95\] I have a problem with this solution, I don't understand where the area between 0 and...

Homework Statement Ok, so in a lab I was preforming Izod impact tests on notched polymer specimens. To complete my calculations I need to determine the correct cross-sectional area to use (Which is baffling me as the simple things usually do) The sample was loaded with the notch facing...

What is the Rate of change of area of circle in respect to radius when radius is 3in I know that that dA/dr is equal to the circumference of the circle But where does that come from? Also the formula for the circumference of the circle is 2(pi)r But the answer is 6 (pi)in^2/in. I understand...

The problem is: Consider the area under the curve f(x)=2x-x2 and above the x axis. Find the equation of the line through the origin that cuts this area into two equal parts.

1. The problem For sake of format I attached the a screenshot of the course material I'm having difficulty wrapping my walnut around. Which is how: Total Displacement = Area of Triangle + Area of Rectangle or Δvector d = Atriangle + ARectangle or Δvector d = 1/2 (V2-V1)Δt +V1*Δt...

If I have a problem in which the laminar/turbulent transition point is said to be 50% the mean aerodynamic chord, how can I find the area of the wing over which there is laminar flow? Is it simply half the wing area?

Show that the curve $x^3+3xy+y^3=1$ has only one set of three distinct points, $P$, $Q$, and $R$ which are the vertices of an equilateral triangle, and find its area.

I have to find the area of the loop of the curve $$a^4 y^2=x^4(a^2-x^2).$$ I have confusion regarding the shape of the graph the limits of integration.

Here's the problem I was given: Find the area of the surface generated by revolving the curve $$x=\frac{e^y + e^{-y} }{2}$$ from 0 $$\leq$$ y $$\leq$$ ln(2) about the y-axis. I tried the normal route first... g(y) = x = $$\frac{1}{2} (e^y + e^{-y})$$ g'(y) = dx/dy = $$\frac{1}{2} (e^y -...

Homework Statement Find the area of the surface generated by revolving the curve x=\frac{e^y + e^{-y} }{2} from 0 \leq y \leq ln(2) about the y-axis. The Attempt at a Solution I tried the normal route first... g(y) = x = \frac{1}{2} (e^y + e^{-y}) g'(y) = dx/dy = \frac{1}{2}...

Hello, I am looking for an help about this, I have very short time to do many of them and those are an example, could someone show me one solution or explain me how to do it? Thank you if you can help me, I really appreciate. Francesco.