# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | June | Q#7

Hits: 19

Question

a)   Show that  can be written as .

Given that , , and that  at ,

b)  Find y in terms of x.

Solution

a)

We are given;

We have the algebraic formula;

b)

We are required to find y in terms of x, when;

We are also given that , and that  at .

Clearly it is the case of finding equation from its derivative.

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

For the given case;

From (a) we know that;

Therefore;

Rule for integration of  is:

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 also given that , and that  at .

Therefore, substituting given values of y and x.

Hence, above equation obtained from integration can now be written as;