Question

A curve for which  passes through . Find the equation of the curve.

Solution

i.
 

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

We are given that;

Therefore;

Rule for integration of  is:

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 that curve passes through . Therefore, we can substitute its coordinates in the  above obtained equation.

Hence equation of the curve is;