HELP- DISK METHOD CALCULUS

Question

By using the disk method, find the volumes of the solids generated by revolving the regions bounded by the given lines and the curves about the x-axis. (So the axis of revolution for both parts below is the x-axis).

a. y= x^2+ 1 , y=x+3

b. y= 2√x , y=2 , x=0

Answer 1

a. v = π∫_-1²[(x + 3)² - (x² + 1)²]dx = π∫_-1²((6x - x² - x⁴ + 8)dx = π(3x² - x³/3 - x⁵/5 + 8x)_-1² = π[(12 - 8/3 - 32/5 +

16) - (3 + 1/3 + 1/5 - 8)] = 117π/5; x² + 1 = x + 3; x = -1 or x = 2∫

b. v = π∫₀¹(2² - 4x)dx = π(4x - 2x²)₀¹ = 2π; 2√0 = 0; 2√x = 2; x = 1