Question

A curve is such that  . Given that the curve passes through the point , find the

  equation of the curve.

Solution

We are given that curve  passes through the point  and we are required to find the  equation of the curve.

We can find equation of the curve from its derivative through integration;

For the given case;

Therefore;

Rule for integration of  is:

If a point   lies on the curve , we can find out value of . We substitute values of  and   in the equation obtained from integration of the derivative of the curve i.e. .

 

We are given a point on the curve . Substituting these values of x & y coordinates of the point  we can find .

Hence we can write the equation of the curve as follows;