Final answer:
To find the area of the region in the first quadrant bounded by the line y=1, the curve x = y^(3/2), and the y-axis, we need to calculate the area under the curve between the y-axis and the curve x = y^(3/2).
Step-by-step explanation:
To find the area of the region in the first quadrant bounded by the line y = 1, the curve x = y3/2, and the y-axis, we need to calculate the area under the curve between the y-axis and the curve x = y3/2.
Since y = 1 is a horizontal line, the area under the curve is formed by the integral of x = y3/2 with respect to y from y = 0 (where it intersects the y-axis) to y = 1 (where it intersects the line y = 1).
The integral is given by A = ∫ (x = y3/2 ) dy. Solving this integral will give us the area of the region.