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# Intergration Watch

1. 7.

The diagram above shows the line with equation y = 9 – x and the curve with equation y = x2*– 2x + 3. The line and the curve intersect at the points A and B, and O is the origin.
(a) Calculate the coordinates of A and the coordinates of B.
(5)
The shaded region R is bounded by the line and the curve.
(b) Calculate the area of R.
2. (Original post by Nelson199)
7.

The diagram above shows the line with equation y = 9 – x and the curve with equation y = x2*– 2x + 3. The line and the curve intersect at the points A and B, and O is the origin.
(a) Calculate the coordinates of A and the coordinates of B.
(5)
The shaded region R is bounded by the line and the curve.
(b) Calculate the area of R.
You haven't actually said which part you're stuck with?

For a) put the two equations equal to each other, get equal to zero by taking everything across to one side, then factorise, which will give you your x co-ordinates and then sub these values into y=9-x to get your y co-ordinates.

For b) you integrate the two line equations, between the two x values you calculated in part a, then subtract the smaller value from the larger, and that will be the area of the shaded region.

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