2
votes
1answer
22 views

differential in integration cancelled but variable endpoint is changed

In kinetic energy equation in wiki. I have difficulty problem how endpoint in integral change from t to v. This doesn't look like it is using substitution method. ...
2
votes
0answers
75 views

Could this be called Renormalization?

Quoted from   Space-Time Approach to Quantum Electrodynamics   by R. P. Feynman, Phys. Rev. 76, 769 1949 : We desire to make a modification of quantum electrodynamics analogous to the ...
0
votes
0answers
49 views

Integral of P(x)/(A(x)E(x)

I have a question where I have to use the formula $\delta = \int_0^L \frac{P(x)}{A(x)\epsilon(x)}$. It is used to find the 'displacement' or the 'elastic deformation' of an axially loaded member like ...
0
votes
1answer
60 views

Using definite integrals with velocity and acceleration

Rocket A is traveling 49 ft/sec at 80 seconds. Rocket B is launched upward with an acceleration of $$a(t)=\frac3{\sqrt{t +1}}$$. At time t=0 seconds, the initial height of the rocket is 0 feet, and ...
1
vote
1answer
364 views

Pumping Water out of Parabolic tank?

First of all, I understand how to do the integration part of this problem, but I am confused about the setup. Here is the question: Use integration to find the work done pumping all the water ...
4
votes
1answer
113 views

Integral evaluation

Evaluate $$\int_{0}^{2\pi}\int_{0}^{\pi} {\cos\phi \sin\phi \over \sqrt{R^2+r^2-2Rr(\cos\phi \cos\theta+\sin\phi \sin\theta \cos\psi )}} d\phi\ d\psi$$ where $R,r,\theta$ are all constants. ...
-1
votes
1answer
54 views

Moment of inertia of a n-dimensional sphere

Is it well known that the moment of inertia of a sphere can be calculated starting from its density $\rho=\frac{m}{V}$ where $V$, the volume of the solid is: $V=\frac{4}{3}\pi r^3$. Calling it $I_3$, ...
0
votes
1answer
55 views

Zero velocity field inside an ellipse

I'm investigating the velocity field induced by a continuous distribution of 2D vortex points distributed along an ellipse $\{a\cos\theta,b\sin\theta\}$. I'm interested in the field inside the ...
2
votes
1answer
93 views

Is $f''(f)df=f'(x)df'$ correct?

This question is about kinematics and $a , v, x$ stand respectively for acceleration, velocity, position. Supposing we have an expression of $a$ in function of $x$, we have the following theorem: ...
1
vote
1answer
198 views

Help with integral for electric potential

I need help evaluating the following integral $$\frac{ \sqrt 2 \sigma}{2 \epsilon_0} \int_0^R \frac{r \,dr}{ \sqrt{(z- \frac{ rh}{R} ) ^2 + r^2} }$$ This integral pertains to the Electric potential ...
1
vote
1answer
1k views

Surface area , center of mass, and moment of inertia of paraboloid

I have done a bunch of work and simply wish to check that it makes sense. I have a hollow parabola of height b and base radius b ($ z = \frac{x^2 + y^2}{b}$ bounded by z = b) 1) surface area of ...
3
votes
4answers
1k views

Hydrostatic pressure on a square

Vertically inserted into the water I have a rectangle 6 feet wide and 4 feet high that is submerged under the water with 2 feet of water above it. Using a riemann sum how do I find the pressure? I ...
-2
votes
1answer
164 views

Precision and time of calculating the integral in Mathematica

1)How to calculate this integral, because I have some very small values (10^-20) in solution and values on this position in matrix should be equal to zero. If I can not do that with working precision, ...