Sketch the area of the region bounded by the curves y= squareroot of(x+1); x — axis; y — axis; x = 8?

Question

Sketch the area of the region bounded by the curves y= squareroot of(x+1); x — axis; y — axis; x = 8?

Answer 1

y=sqr(x+1)

y^2 = x+1 is a rightward opening parabola with vertex (-1,0)

y =sqr(x+1) is the top half of that rightward opening parabola

when x=8, y = sqr(8+1) = sqr9 = 3

integral of (x+1)^.5 =((x+1)^1.5)/1.5

evaluated from 0 to 8 is

(2/3)(9)^(3/2) = (2/3)3(9) = 18