The equation of curve whose slope is given by $\frac{dy}{dx}=x$ and which passes through $(1,\frac{5}{2})$ is :
Answer & explanation
Correct answer: option 2
The correct answer is option (2) → $y =\frac{x^2}{2}+2$
$\frac{dy}{dx}=x⇒∫dy=∫xdx$
so $y=\frac{x^2}{2}+C$ putting $(x, y) = (1, 5/2)$ to get C
$⇒\frac{5}{2}=\frac{1}{2}+C$
$⇒C=2$
$⇒y=\frac{x^2}{2}+2$