# Thread: area under a curve as the limit of a sum of areas

1. ## area under a curve as the limit of a sum of areas

A curve has a gradient function of $3x^2-2x+5$.Given that the curve passes through the point $(0,2)$,find the equation of the curve.

please show me the step by step..

2. Originally Posted by mastermin346
A curve has a gradient function of $3x^2-2x+5$.Given that the curve passes through the point $(0,2)$,find the equation of the curve.

please show me the step by step..
This isn't finding an area, it's finding an antiderivative...

The function you are looking for is:

$f(x) = \int{3x^2 - 2x + 5\,dx}$

$= x^3 - x^2 + 5x + C$.

Now using the fact that $(0, 2)$ lies on the curve:

$2 = 0^3 - 0^2 + 5\cdot 0 + C$

$2 = C$.

So the function is

$f(x) = x^3 - x^2 + 5x + 2$.