Integration HSC 2005 Question (1 Viewer)

[RivalryofTroll]

The shaded region in the diagram is bounded by the circle of radius 2 centred at the origin, the parabola y = x^2 - 3x +2, and the x-axis. By considering the difference of two areas, find the area of the shaded region.

 

[RealiseNothing]

Area of that part of the circle minus the area under the parabola.

 

[RealiseNothing]

 

[RivalryofTroll]

Answer says:
(6pi -5)/6

cant get it.

 

[RivalryofTroll]

nvm i got it.

thanks.

 

[D94]

Answer says:
(6pi -5)/6

cant get it.

That's the same as pi - 5/6.

The area of the quadrant is pi, (you can get this from knowing the area of a circle, then finding a quarter of it). The area between the parabola, the x and y axis is the integral of x<sup>2[/sup - 3x + 2 wrt x, which is x3/3 - 3x2/2 + 2x from 0 to 1. This equals 1/3 - 3/2 + 2 = 5/6.

So for the shaded region, you want to remove the parabolic section from the quadrant, hence giving the result pi - 5/6 = (6pi - 5)/6</sup>