Question

Integral of x=y^2?

Answer 1

(1/3)y^3

Answer 2

with respect to x *

Answer 3

oh so then is the question integral sqrt(x) dx ?

Answer 4

\[x=y^2\]
\[\int x\text dx=\int y^2\text dx\]
\[\frac {x^2}2=y^2x+c\]

Answer 5

hmmm i think have made a false assumption
\(y=y(x)\)

Answer 6

\[y^2=x\]\[y=\pm \sqrt x\]

\[\int y\text dx=\int\pm\sqrt x\text dx\]\[xy=\pm\int x^{1/2}\text dx\]\[xy=\pm \frac{x^{3/2}}{3/2}+c\]\[xy=\frac 23x^{3/2}+c\]\[y=\frac 23 x^{1/2}+c\]\[y=\frac 23 \sqrt{x}+c\]

Answer 7

ops
\[xy=\pm\frac 23 x^{3/2}+c\]\[y=\pm\frac 23\sqrt x+\frac cx\]