area between curves 20.2

Question

f(x)=x⁴-8x³+18x² ,g(x)=-25x+102

the area is ______

Answer 1

x⁴ - 8x³ + 18x² = - 25x + 102; x⁴ - 8x³ + 18x² + 25x - 102 = 0; x = 3 or x = - 2.

We applied rational zeros theorem.

Area A = ∫_-2³(- 25x + 102 - x⁴ + 8x³ - 18x²)dx = (-25x²/2 + 102x - x⁵/5 + 2x⁴ - 6x³)_-2³ = 312.5