# Thread: 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 $\displaystyle \frac{dy}{dx}\ = - \frac{k}{k^3}$ 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 $\displaystyle y = \frac{16}{x^2}\ +2$

2. Originally Posted by pederjohn
Hi

another q.

The diagram shows a curve for which $\displaystyle \frac{dy}{dx}\ = - \frac{k}{k^3}$ 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 $\displaystyle y = \frac{16}{x^2}\ +2$
I assume you mean
$\displaystyle \frac{dy}{dx}\ = - \frac{k}{x^3}$
$\displaystyle \Rightarrow y = -k\int x^{-3}dx$
$\displaystyle =-k\frac{x^{-2}}{(-2)}+c$

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

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

Can you complete it now?