Final answer:
To find the region bounded by the curves y = √x and y = x²/8, we need to calculate the area between these two curves. The region bounded by the curves and the x-axis is the area under the curve y = x²/8 from x = 0 to x = 4. The region bounded by the curves and the y-axis is the area under the curve y = √x from x = 0 to x = 64.
Step-by-step explanation:
To find the region bounded by the curves y = √x and y = x²/8, we need to calculate the area between these two curves.
a. To find the region bounded by the curves and the x-axis, we need to find the x-values where the curves intersect. Setting √x = x²/8, we get x = 0 or x = 4. Therefore, the region bounded by the curves and the x-axis is the area under the curve y = x²/8 from x = 0 to x = 4.
b. To find the region bounded by the curves and the y-axis, we need to find the y-values where the curves intersect. Setting √x = x²/8, we get x = 0 or x = 64. Therefore, the region bounded by the curves and the y-axis is the area under the curve y = √x from x = 0 to x = 64.