Showing all working, determine whether the following improper integral exists

Question

Showing all working, determine whether the following improper integral exists and if so, find its value

I = ∫ 2/sqrt(x + 5) dx from -5 to 5

Answer 1

I = 2∫dx ⁄ √(x+5) from –5 to 5 Let u = √(x+5), x+5 = u², dx = 2udu, dx ⁄ √(x+5) = 2udu/u = 2du

So I = 2∫dx ⁄ √(x+5) from –5 to 5 = 2∫2du from √(–5+5) to √(5+5)

I = 4∫du from 0 to √(10) = 4√(10) – 0

Answer

I = 4√(10)