# Math Help - show by intergration that the equation of the curve is y=...

1. ## show by intergration that the equation of the curve is y=...

Hi

another q.

The diagram shows a curve for which $\frac{dy}{dx}\ = - \frac{k}{k^3}$ where k is a constant. the curve passes through the points (1,18) and (4,3).

Show by intergration that the equation of the curve is $y = \frac{16}{x^2}\ +2$

2. Originally Posted by pederjohn
Hi

another q.

The diagram shows a curve for which $\frac{dy}{dx}\ = - \frac{k}{k^3}$ where k is a constant. the curve passes through the points (1,18) and (4,3).

Show by intergration that the equation of the curve is $y = \frac{16}{x^2}\ +2$
I assume you mean
$\frac{dy}{dx}\ = - \frac{k}{x^3}$
$\Rightarrow y = -k\int x^{-3}dx$
$=-k\frac{x^{-2}}{(-2)}+c$

$=\frac{k}{2x^2}+c$

Plug in the two pairs of values $(1, 18)$ and $(4,3)$, and solve the resulting simultaneous equations for $k$ and $c$.

Can you complete it now?