Let R be the region bounded by the X - axis, the graph of y=Sqrt (X+1) and the line x=3. Find the area of the region R.

1) Such area is the area under the curve y = √ (x+1) from x=-1 to x=3

2) Such area is the inegral fo the function y = √ (x+1) from x = - 1 to x=3

3) ∫ (√ (x+1) = [2/3] (x + 1) ^ (3/2) | from x = - 1 to x = 3

[2/3] { (3+1) ^ (3/2) - (-1 + 1) ^ (3/2) = [2/3] { √ (64) - 0) } = 16/3 = 16/3

Answer: 16/3