Area Definition and 1000 Threads

The "s" in the geodesic equation refers to the "surface area" for that portion of the orbit around a star or black hole. For a small enough "delta t" the surface areas are the same. Around a small star the orbital surface area (without the other interfering gravitational sources) would...

Homework Statement ∫(a= -3 , b= 0) (1 + √9 - x^2) dx Homework Equations ∫(a,b) f(x) dx = lim as n → \infty \sum f(xi) delta x The Attempt at a Solution I tried plugging in my a and b value into the function just as I would with any other function to find the area and i get a number...

Homework Statement For the 1st one you wouldn't really need MATLAB I guess to find the area under the curve, it is 0 and so is its energy. For the 2nd one I got A=1.73 and so E=2.99.Homework Equations area under curve = evaluate integral from t=t1 to t=t2. in this case t=-2 to t=5 since they...

Find the area bounded by the curves $$y = x^2[/math] and [math]y = 2x - x^2$$so $$ x^2 = 2x - x^2$$ $$ 2x - x^2 - x^2 = 2x - 2x^2$$ So then would I factor out a 2 and get $$ 2x(x - 1)$$ $$ x = 1$$ So the $$\int ^1_0 Right - left \, dx$$

Homework Statement A typical adult burns about 2500 Calories in one day. 1)How much energy does the average human emit every second 2)What is another term to use for expressing a “Joule per second”? 3)From your answers to (1) and (2), you just determined the “luminosity” of the average human...

Hello, quick question really. Homework Statement Find the area bound by the x axis, x = 1, x = 4 and y = 2/x Homework Equations The Attempt at a Solution Representing this graphically, the question is equivalent to performing the definite integral of y = 2/x from 1 to 4. Right? Which...

Homework Statement The figure shows a semicircle with radius 1, horizontal diameter , and tangent lines at and . At what height above the diameter should the horizontal line be placed so as to minimize the shaded area http://imgur.com/grrCqWF Homework Equations The equation of a...

consider the following image (the red is the surface area element and the green is the differential element that I'm integrating over) when we derived this in class, we treated the area formed by vectors a and b, as the area of a parallelogram. the thing is, a and b should be at right...

So it's been a while since I've done one of these problems. Need to make sure I am using the right procedures to solve it. Q)Find the area bounded by the curve $y = \frac{1}{2}x^2$ and $x^2 + y^2 = 8$ So first thing I did was plug in numbers to get the two graphs. It looks like they intersect...

I an ideal gas how do I calculate the number of collision per unit area? By collision I do not mean collision between the atoms but rather it is a problem where I know that a nucleation cluster of area A is in my gas, and I want to find the probability that it will get hit by an atom. I know the...

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

Homework Statement Obtain the surface area when the curve y=ex, 0≤x≤1, is rotated about the x-axis Homework Equations Surface Area = 2∏a∫b x√(1+(dy/dx)2)dx The Attempt at a Solution I started with the the equation, Surface Area = 2∏0∫1 x√(1+e2x)dx. However, whichever way I try to...

Homework Statement The shaded band shown here is cut from a sphere of radius Rby parallel planes hunits apart. Show that the surface area of the band is 2piRh. The image is on this site: http://imgur.com/TCx1weD http://imgur.com/TCx1weD The Attempt at a Solution How do I do...

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

Finding the area of an irregular polygon with n side is quite easy when we are given the length of all of the n sides and the length of (n-3) specific diagonals. This way, we get (n-2) triangles whose areas can be calculated using Heron's formula and then added up. But what if the length of...

I am trying to calculate the friction factor for a Fanno flow in a constant area duct. I know the friction factor is based on Reynolds number however does the Reynolds number not vary along the pipe due to a change in dynamic viscosity? (caused by a decrease in temperature along the pipe). And...

Here's my work: http://i.imgur.com/UMj72Ub.png I used the surface area differential for a parametrized surface to solve for the area of that paraboloid surface. My friend tried solving this by parametrizing with x and y instead of r and theta which gave him the same answer. I would greatly...

Hi! Say I have a region described by any number of inequalities. This region is a surface in 3D space. How can I ask Mathematica to calculate the region's area? If it helps, my particular region is the intersection of a hollow sphere and a solid (i.e. filled-out) toroid-like surface. I'm...

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

if I have a sinusoidal trace on an oscilloscope (v vs t) and I wanted to find the area under the wave form squared graph I could integrate the sqaured waveform with respect to t. but since i don't have the integration facility... is it fair to say that the area under the graph is proprtional...

In some parts of the physics,sometimes it happens that the volume of a region of space or the area of a surface enters into a formula.In such situations,most of the time,the author argues that "although I have derived this formula for such a shape,it is independent of the shape of the...

When doing surface integrals of surfaces described parametrically, we use the area element dA = ndS = (rv x rw)dvdw Where dS is the surface area element and v and w are the parameters. I'm fine with the derivation of this (I think) but I don't understand why it's necessary to have n and dS...

If someone wanted to go into computational physics, would that be the PhD area of study, or is it just a branch of the better known areas, like hep, condensed matter, etc. Also is it considered theoretical or experimental? (I would assume experimental). Thanks!

Homework Statement The aerodynamic drag on an object moving through air is proportional to Av^2, where A=cross-section, and v=velocity. The terminal velocity of a person without a parachute falling through the air is about 56m/s. Estimate the area of the cross-section of a person seen from the...

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

I am majoring in Mechanical Engineering, and I found a research opportunity I really want (it focus on Fastening and Joining). I want to take classes relevant to this area, but my university offers different areas to specialize in as an Undergrad, so which one should I focus on in order to take...

Problem: Calculate the area of region defined by the inequalities: $$-1<xy<1$$ $$-1<x^2-y^2<1$$ Attempt: Although I have solved the problem but I am not very satisfied with the method I used. The graph of region is symmetrical in all the four quadrants so I calculated the area in the first...

I want to know how people usually choose their area of research?Is it just interest?What about choosing between areas which are all of your interest? I know,it may seem weird for an undergrad to ask that,but I think its the time for me to decide on it.Because I started studying physics when I...

Homework Statement Suppose C:y=f(x) with f a twice-differentiable function such that f''(x)> 0 for each x on the closed interval [0,a] where a is a positive constant. Suppose T is the tangent line to C at a point P= (r,f(r)) on C where r is in the open interval (0,a). Let A be the area of the...

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

I've been trying to figure out what a negative area means, but I can't. Homework Statement Calculate the area between f(x) = 3^{x} \, , \, g(x)=2x+1 The attempt to a solution The intersections are located in x=0 and x=1. So I do the integral from 0 to 1. \int_{0}^{1} (g(x)-f(x))dx =...

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

Homework Statement f(x) = 1/x Interval [1, ∞) about the x-axis Set-up the integral for the surface area of the solid Then use the substitution u = x2 and integrate using the formula: ∫ sqrt(u2 + a2) / u2 du = ln(u + sqrt(u2 + a2) - sqrt(u2 + a2) / u + C a is a constant Homework...

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

Hello all! New to the forums, and I have a question for you. In my classes, we have been dealing a lot with proofs lately, so when I was working on an assignment, I figured I would try and find my own proof for something, just for the hell of it. I decided to tacle the area of a right angled...

Homework Statement My apologies in advance for the messiness of the equations; the computers available to us do not correctly process the LaTex code. I am tasked with estimating the area under the curve f(x)=x2+1 on the interval [0,2] using 16 partitions. Online calculators and my...

Homework Statement I understand how to determine the direction on rectangular surfaces, however when it comes to a cylinder or sphere or, in the case of the problem i am working on now, for a long rod that has been bent around in a circle i.e a a rectangular ring, I don't know what to do.

Homework Statement Find the maximum area of a triangle with sides a\in (0,1] ,b\in [1,2], c\in [2,3]. Homework Equations The Attempt at a Solution I tried to make the area as a function of a single variable so that by differentiating I can get the answer. But it was...

A line divides an equilateral triangle into two parts with the same perimeter and having areas $A_1$ and $A_2$ respectively. Prove that $\dfrac{7}{9} \le \dfrac{A_1}{A_2} \le \dfrac{9}{7}$.

I've found a formula for the area of a regular hexagon,but it seems to falter when i try to finds its area using the apothem sometimes,i know the formula is not wrong because i derived and verified it's authenticity so that can't be it. I heard that by not utilizing the apothem formula, you...

I have to calculate the surface area limited with two functions: $$g(x)=2$$ and $$h(x)=\frac{4}{4x^2+1}$$ i was thinking first to calculate the points where this functions are intersecting by $$g(x)=h(x)$$ and to find corresponding $x$ for the intersection...and then to calculate definite...

In my high school Calculus course, I've encountered several optimization problems involving the area of a circle and I noticed the obvious fact that if you differentiate the area of a circle you obtain the expression for its circumference. This implies that the rate of change of a circle's area...

For question 16, I am having trouble assessing the question. I set the sides equal to x and put the image in the middle of a coordinate axes hoping it would be easier to assess. I also set r2 = [(1/2)x]2 + y2 and tried to set up an integration but cannot come up with a relation for the inner...

This is a problem from Tom Apostol's calculus book (the very first problem set in the introduction). It wants you to find $$\int_0^b (ax^m+c)\,dx$$ using Archimedes' method of exhaustion. I'm attaching a diagram and a pdf of my work for the problem since it's rather involved. I'm doing this...

Find the area of the indicated region. so right minus left so I know the first thing I need to do isfind the integrals so $$\frac{x^2}{8} + 1 = x - \frac{1}{2}$$ So I took a stab at this and got this.. $$\frac{x^2}{8} - \frac{8x}{8} + \frac{12}{8}$$ $$x^2 - 8x + 12 = (x - 6) (x - 2) = x =...

I have the region r = 2 + cos(theta) . I know the area should be 18.64. I set it = 0 and then solve for theta. So theta = 0 and theta = 2pi I set up my integral [0, 2pi] 1/2(r)^2 dThetaA After simplification I got 1/4 integral cos2theta + 4costheta + 5 but my answer does not come out right...

Find the area bounded by the curve $$x = 6x - x^2$$ and the y axis. So can I use the even function rule to get: $$2 \int^2_0 6x - x^2 dx$$ I just need someone to check my work. $$2 [ 3x^2 - \frac{1}{3}x^3 ] | 2, 0$$ $$ 2 [ 12 - \frac{8}{3}]$$ $$2 [ \frac{36}{3} - \frac{8}{3} ]$$ $$2 * 28/3$$...

Find the values of c such that the area of the region bounded by the parabolas y = x2 - c2 and y = c2 - x2 is 576. Attempt: 576 = -cc∫-x2 + c2 - (x2 - c2) dx 576 = 2-cc∫c2 - x2 dx 576 = c2x -(1/3)(x3) l0c *I know by symmetry that the area of 0 → c is half the area of -c → c 576 = c3 -...

Consider the area between the curve $$y = x^2 + 2x$$ from $$x = 1$$ to $$x = 5.$$ Approximate the area of the region by using a regular partition of 4 sub intervals. a) using L4 i,e, left hand endpoints b) using R4 i,e, right hand endpoints So for the left hand endpoints would I just plug...