!!! PLEASE HELP !!!

Question

1. Calculate the integral:
2. Determine the area of the region bounded by the following curves below. Sketch the region complete with their points of intersection (if there is):

Answer 1

1. ∫₂^∞dx/(x√x² - 4) = lim ε→0∫_2+ε³dx/(x√x² - 4) + lim A→∞∫₃^Adx/(x√x² - 4) = lim ε→0 1/2sec^-1Ix/2I_{2 + ε}³ +

lim A→∞1/2sec^-1Ix/2I₃^A = lim ε →0[1/2sec^-1I3/2I - 1/2sec^-1I(2 + ε)/2] + lim A → ∞ [1/2sec^-1IA/2I -1/2sec^-1I3/2I] = lim A → ∞ 1/2sec^-1IA/2I - lim ε → 0 1/2sec^-1I(2 + ε)/2! = 1/2sec^-1(∞) - 1/2sec^-1(1) = 1/2·π/2 - 1/2·0 = π/4.

2.x - coordinates of points of intersection: x³ = 4x; x = 0, x = ±2.

So, area A = ∫_-2⁰(x³- 4x)dx + ∫₀²(4x - x³)dx = (x⁴/4 - 2x²)_-2⁰ + (2x² - x⁴/4)₀² = 0 - 4 + 8 + 8 - 4 - 0 = 8