Question

The region R is bounded by the curve $y =4-x²$ and the line $y=4-2x$

   a. Find the intersection points.

b.Sketch and shade the region R.

Answer 1

a. intersection points we can find from equation

$4-x^2=4-2x$

$x^2-2x=0$

$x(x-2)=0$

$x_1=0$

$x_2=2$

$y_1=4-x_1^2=4-0=4$

$y_2=4-x_2^2=4-4=0$

Answer: intersection points: (0, 4), (2, 0).

b.