- #1
matt_crouch
- 161
- 1
so
## \int wdw = \frac{1}{2}w^{2} ##
now if w=x+y,
## \int (x+y)(dx+dw)= \int xdx + \int ydx + \int xdy + \int ydy ##
which can be evaluated and gives
##\int(x+y)(dx+dy)=\frac{1}{2}x^{2}+2xy+\frac{1}{2}y^{2}##
but
##\frac{1}{2}x^{2}+2xy+\frac{1}{2}y^{2} \neq \frac{1}{2}w^{2}##
can someone explain why?
## \int wdw = \frac{1}{2}w^{2} ##
now if w=x+y,
## \int (x+y)(dx+dw)= \int xdx + \int ydx + \int xdy + \int ydy ##
which can be evaluated and gives
##\int(x+y)(dx+dy)=\frac{1}{2}x^{2}+2xy+\frac{1}{2}y^{2}##
but
##\frac{1}{2}x^{2}+2xy+\frac{1}{2}y^{2} \neq \frac{1}{2}w^{2}##
can someone explain why?
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