Question

Can somebody check if this is true?
@amistre64

Answer 1

i dont think so, a change of variables is a little more complicated than what you are originally led to believe. It actually introduces a Jacobian into the mix to equate the change from one to the other

Answer 2

Yea okay i hoped i was able to follow a therom in my book for this. but seems not.. okay in that case i am on deep waters.

Answer 3

to dbl chk tho: the volume of a sphere is 4pi/3 when the radius is 1, half of that is 2pi/3

Answer 4

what is the thrm in the book by chance?

Answer 5

It is about iterated integrals. and states;
"if a set called R is defined in the following way:
\[R=(x,y,z)|a \le x \le b, u(x) \le y \le o(x), b(x,y)\le z \le t(x,y) \]
then you write the intergral [inset long equation]

Answer 6

but when i come to think of it.. it is not standing on that form

Answer 7

guess you have to use transformation then?

Answer 8

it does look to be using a sort of substitution in place of the actual limits.

Answer 9

did it say to use this? or were you just taking a stab at it?

Answer 10

the task is just "find the volume useing Infinitesimal calculus (integral calculus)"

Answer 11

last part of the thermo btw: the equation:

Answer 12

becasue of symmetry 1/4 of the volume can be determined; and we can try these limits of integration i spose

a < x < b
0 1

sin(a) < y < sin(b)
sin(x) 0

cos(a) < z < cos(b)
0 cos(x)

but its been too long for me to be sure

Answer 13

it seems to me like that thrm is more along the lines of
\[x=0~to~1\]\[y=0~to~x \]\[z=0~to~\sqrt{1+x^2+y^2}\]

Answer 14

Hmm they also ask me to find the spherical coordinates (forgot to tell sorry)

Answer 15

but that have we done already

Answer 16

but i just don't think they asking me do something not related to the intergral.

Answer 17

\[\int\limits_{0}^{1}(\int\limits_{0}^{x}(\int\limits_{0}^{\sqrt{1+x^2+y^2}}(y)dz)dy)dx \approx 0.228\]

Answer 18

abt 0.64 is what i get from that

Answer 19

times 4 which of course doesnt get us to something sloe enough to 2pi/3

Answer 20

heheh, lets try 1-x^2-y^2 in place of the +s ;)

Answer 21

what about this?
http://en.wikipedia.org/wiki/Spherical_coordinate_system#Integration_and_differentiation_in_spherical_coordinates

Answer 22

seems like r^2 is multiplyed on the function so that y is p^3y insted