Question

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.

Answer 1

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