Integrating f(x,y,z): Confirm Ranges for x, y, z

  • Thread starter Thread starter naspek
  • Start date Start date
  • Tags Tags
    Integrating
naspek
Messages
176
Reaction score
0

Homework Statement



f(x, y, z) = x^2 ; G is tetrahedron bounded by the coordinate planes and the plane octant with equation x + y + z = 1

∫ ∫ ∫ x^2 dzdydx

I try to set up the ranges for x, y and z..

x+y+z = 1
z = 1-x-y...set the limits for z from z=0 to z = 1-x-y

x+y+z = 1
if, z = 0, y = 1-x ...set the limits for y = 0 to y = 1-x

x+y+z = 1
if, z = 0 , y = 0 ...x = a set the limits from x = 0 to x =1

first.. i need help to confirm that my ranges are correct..
because.. I've done the integration and got the wrong answer..
i've double checked my integration and it is right..
there must be something wrong with my ranges.. i guess...
 
Physics news on Phys.org
They look right to me. Why don't you show what you did. It may be an integration error.
 
yup2.. it's integration error.. duuhh...~
thanks btw..
problem solved..
 

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...
View full post »

Similar threads

Proof given ##x < y < z## and a twice differentiable function
Replies
8
Views
1K
Find the constrained maxima and minima of ##f(x,y,z)=x+y^2+2z##
Replies
2
Views
1K
Prove if ##x<0## and ##y<z## then ##xy>xz## (Rudin)
Replies
2
Views
2K
Obtain a nonzero solution of ##y''-4y'+x^2(y'-4y)=0## by inspection
Replies
7
Views
2K
Triple Integral To Find Volume Between Cylinder And Sphere
Replies
2
Views
2K
Calculus ## G(y, z)=z\frac{\partial}{\partial z}F(y, z)-F(y, z) ##?
Replies
6
Views
2K
Proving Irregularity of {(x, y, z) within R^3 : x^2 + y^2 - z^2 = 0}
Replies
14
Views
3K
Lagrange multipliers understanding
Replies
8
Views
2K
Is f(z) =(1+z)/(1-z) a real function?
Replies
17
Views
3K
Prove if ##a\cdot c = b \cdot c## then ##a = b## using Peano postulates
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top