Sketch the area of the region bounded by the curves y= x^2 — 2x + 3; x — axis; x = —2; x = 1?

Question

Sketch the area of the region bounded by the curves y= x^2 — 2x + 3; x — axis; x = —2; x = 1?

Answer 1

x^2 -2x +3 is an upward opening parabola, with vertex = minimum point V(1,-2) y intercept = 3

no x intercepts. It's entirely above the x axis

integral is x^3/3 -x^2 +3x

evaluated from -2 to 1 is

1/3-1 +3 - (-8/3-4-6)

= 7/3 -(-38/3)

= 45/3

= 15