find the area of the region bounded bye the graphs of these equations;

Question

y=2-x^2 and y=x? 

 

 

Answer 1

The curve equation y = 2 - x² and y = x

Equate the y forms.

2 - x²  = x

x² + x - 2 = 0

x² + 2x - x - 2 = 0

x(x + 2) - 1(x + 2) = 0

(x + 2)(x - 1) = 0

x + 2 = 0 and x - 1 = 0

x = - 2 and x = 1

So the limits are - 2 and 1.

Formula for the area

Where f(x) ≥ g(x)

f(x) = 2 - x², g(x) = x

Area is 4.5 square units.