# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/11) | Q#7

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Question The diagram shows parts of the curves and , intersecting at points A and  B.

i.       State the coordinates of A.

ii.       Find, showing all necessary working, the area of the shaded region.

Solution

i.

It is evident that point A is the intersection point of the two curves given by equations;  It is also evident from the equation that point A is the x-intercept of both the given curves.

Therefore, we can find the coordinates of point A as x-intercept of a curve rather easily.

The point at which curve (or line) intercepts x-axis, the value of . So we can find the  value of coordinate by substituting in the equation of the curve (or line).

We choose; Substituting ;       Hence, coordinates of .

ii.

It is evident from the diagram that; To find the area of region under the curve , we need to integrate the curve from point to along x-axis. We are given equation of curve 1 as;   We are given equation of curve 2 as; Therefore;  It is evident from the diagram that for the shaded region x varies from to .

Therefore;  Rule for integration of is:             