Sponsored links: Algebra eBooks
 

Help Index

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

The Maxima on-line user's manual

Algebra Calculator

Search:

Changevar Calculator

Changevar

Function: changevar (<expr>, <f(x,y)>, <y>, <x>) Makes the change of variable given by <f(x,y)> = 0 in all integrals occurring in <expr> with integration with respect to <x>. The new variable is <y>.

          (%i1) assume(a > 0)$
          (%i2) integrate (%e**sqrt(a*y), y, 0, 4);
                                4
                               /
                               [    sqrt(a) sqrt(y)
          (%o2)                I  %e                dy
                               ]
                               /
                                0
          (%i3) changevar (%, y-z^2/a, z, y);
                                0
                               /
                               [                abs(z)
                             2 I            z %e       dz
                               ]
                               /
                                - 2 sqrt(a)
          (%o3)            - ----------------------------
                                          a

An expression containing a noun form, such as the instances of integrate above, may be evaluated by ev with the nouns flag. For example, the expression returned by changevar above may be

     evaluated by ev (%o3, nouns).

changevar may also be used to changes in the indices of a sum or product. However, it must be realized that when a change is made in a sum or product, this change must be a shift, i.e., i = j+ ..., not a higher degree function. E.g.,

          (%i4) sum (a[i]*x^(i-2), i, 0, inf);
                                   inf
                                   ====
                                   \         i - 2
          (%o4)                     >    a  x
                                   /      i
                                   ====
                                   i = 0
          (%i5) changevar (%, i-2-n, n, i);
                                  inf
                                  ====
                                  \               n
          (%o5)                    >      a      x
                                  /        n + 2
                                  ====
                                  n = - 2

(%o1)                                true
(%i2) 

Changevar Example

Related Examples

changevar-diff-integrate-ratsimp

integrate(x/(x^3+1),x);

ratsimp (diff(integra...

a:integrate(1/((x-3)^...

Calculate

changevar-diff-integrate-ratsimp

integrate(x/(x^3+1),x);

ratsimp (diff(integra...

a:integrate(1/((x-3)^...

Calculate

changevar-diff-integrate-ratsimp

integrate(x/(x^3+1),x);

ratsimp (diff(integra...

a:integrate(1/((x-3)^...

Calculate

changevar-integrate-kill-radcan-sin-tan

kill(all);

changevar(integrate(1...

radcan(%);

Calculate

changevar-inf-integrate-solve-sqrt

'integrate((x+(x^2+1)...

solve(u-(sqrt(x^2+1)+...

changevar(%,u-(sqrt(x...

Calculate

changevar-cos-integrate-logabs-sin-true

logabs:true;

i = 'integrate(1/sin(...

eq:t=cos(x);

Calculate

changevar-cos-erf-integrate-phi-pi-sin

kerf(x):=(sin(theta)/...

I:'integrate(kerf(x),...

I:changevar(I,y-cos(t...

Calculate

changevar-integrate-nouns-sin-tan

changevar('integrate(...

ev(%,nouns);

Calculate

changevar-cos-erf-integrate-phi-pi-sin

kerf(x):=(sin(theta)/...

I:'integrate(kerf(x),...

I:changevar(I,y-cos(t...

Calculate

changevar-integrate-sin-tan

changevar('integrate(...

Calculate