CUET Preparation Today
The equation of curve whose slope is given by $\frac{dy}{dx}=x$ and which passes through $(1,\frac{5}{2})$ is : |
$ y =x^2+\frac{5}{2}$ $y =\frac{x^2}{2}+2$ $ y =\frac{x^2}{3}+\frac{2}{3}$ $y=3x^2+5$ |
$y =\frac{x^2}{2}+2$ |
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 $⇒\frac{5}{2}=\frac{1}{2}+C$ $⇒C=2$ $⇒y=\frac{x^2}{2}+2$ |
