Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer.

Question

Enclosed by y = x^2 − 4x + 1 and y = −x^2 + 4x − 5

Answer 1

the curves intersect at x=1,3 so the area is

∫[1,3] (−x^2 + 4x − 5 )-(x^2 − 4x + 1) dx
= ∫[1,3] -2x^2 + 8x - 6 dx
= -2/3 x^3 + 4x^2 - 6x [1,3]
= 8/3

Answer 2

thank you so much