Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2003 | May-Jun | (P2-9709/02) | Q#3
The diagram shows the curve . The shaded region R is bounded by the curve and by the lines x = 0, y = 0 and x = p.
i. Find, in terms of p, the area of R.
ii. Hence calculate the value of p for which the area of R is equal to 5. Give your answer correct to 2 significant figures.
To find the area of region under the curve , we need to integrate the curve from point to along x-axis.
It is evident from the diagram that area R of shaded region is area under the curve along x- axis from x=0 to x=p.
Rule for integration of , or ;
We are given that;
We have demonstrated in (i) that;
Taking natural log of both sides;
For , , .