Question

Coordinate of P is (1,1) and the coordinate of Q is (2,0). What is the area of the area bounded by the curve `y=2x-x^2`, the straight line `x+y=2` and the y-axis?

Answer 1

The area is `5/6` square units.

Explanation:

We want to integrate on `(0, 1)`. You can see that the linear function is above the quadratic function therefore our area equation will be

`A = int_0^1 2 - x - (2x - x^2) dx`

`A = int_0^1 2 - x -2x + x^2 dx`

`A = int_0^1 x^2 - 3x + 2 dx`

`A = [1/3x^3 - 3/2x^2 + 2x]_0^1`

`A = 1/3(1)^3 - 3/2(1)^2 + 2(1)`

`A = 1/3 - 3/2 + 2`

`A =5/6`

Hopefully this helps!