calculus help

Question

Find the exact area of the region bounded by the curves  y=10x2−12x+10 and  y=9x2−9x+10 . Answer in integer or fraction form.  

NO DECIMAL

APPROXIMATIONS.

The area between the curves is

enter your response here

square units.

Answer 1

10x² - 12x + 10 = 9x² - 9x + 10; x² - 3x = 0; x = 0; x = 3

Area A = ∫₀³(3x - x²)dx = (3x²/2 - x³/3)₀³ = 27/2 - 9 = 9/2.

Answer 2

f(x)=10x²-12x+10

g(x)=9x²-9x+10

f(x)-g(x)=x²-3x=x(x-3)

Intercept points x=0,3

A=∫³₀g(x)-f(x)dx=∫³₀-x²+3xdx=-x³/3+3x²/2|³₀ = -9 +27/2=9/2