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
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.
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).
Hence, coordinates of .
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;
It is evident from the diagram that for the shaded region x varies from to .
Rule for integration of is: