What is the area of the region bounded by the curve y=square root(x-1), y axis and y=1 to y=5 ?

We notice that in this case, we'll have to write a
function of y.

We'll put y =
sqrt(x-1).

We'll raise to sqare both sides to eliminate the
square root:

y^2 = x - 1

We'll
add 1 both sides:

x = y^2 +
1

The area bounded by the curve
is:

Int f(y)dy = F(5) - F(1) (Leibniz-Newton
formula)

Int f(y)dy = Int (y^2 +
1)dy

Int (y^2 + 1)dy = y^3/3 + y +
C

F(5) = (5^3/3 + 5) =
140/3

F(1) = 1/3 + 1 = 4/3

Int
f(y)dy = 140/3 - 4/3 = 136/3

The area bounded
by the given curve, y axis and the lines y = 1 to y = 5 is: A = 136/3 square
units.