Question

If $\frac{dy}{dx}=3x^2$, then $y$ is equal to

• A. $\frac{3x^2}{2}+c$
• B. $x^2+c$
• C. $3x^3$
• D. $x^3+c$

Answer 1

The correct option is D $x^3+c$

We know that,

$\int x^{n}dx=\frac{x^{n+1}}{n+1}+C$

$\therefore dy=3x^{2}dx\int dy=\int 3x^{2}dx=3\int x^{2}dx=3\frac{x^{2+1}}{2+1}+C\{n=2\}y=x^3+C$