A) \[y=\frac{x\left| x \right|}{2}+c\]
B) \[y=\frac{\left| x \right|}{2}+c\]
C) \[y=\frac{{{x}^{2}}}{2}+c\]
D) \[y=\frac{{{x}^{3}}}{2}+c\] Where c is an arbitrary constant
Correct Answer: A
Solution :
[a] \[\frac{dy}{dx}=\left| x \right|\] \[\frac{dy}{dx}=x\] for \[x\ge 0;\] \[\frac{dy}{dx}=-x\] for \[x<0;\] \[\int{dy=\int{xdx}}\] \[y=\frac{{{x}^{2}}}{2}+{{C}_{1}}\] ?. (i) \[\int{dy=-1xdx}\] \[y=-\frac{{{x}^{2}}}{2}+{{C}_{1}}\] ?. (ii) From (i) and (ii) \[y=\frac{x\left| x \right|}{2}+C\]
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