Thus, the volume of the generated solid is

Thus, we have 𝑎 = − 1 and 𝑏 = 4, and the volume of the solid of revolution is given by The upper bound is 𝑥 = 4 and the lower bound is determined by the intersection of the curves 𝑦 = √ 𝑥 + 1 and 𝑦 = 0, which is 𝑥 = − 1 this can also be visualized from the plot of the region bounded by the curves. The limits of the integral, 𝑎 and 𝑏, are determined by the vertical bounds of 𝑥 in the region. Thus, the cross-sectional area is given by

The vertical cross-sectional shape of our solid will be a disk, and the radius of each disk will be the value of the function at that point, 𝑅 = √ 𝑥 + 1. Since we are rotating this region about the 𝑥-axis, the volume is given by This will be determined using integration. Of a region, bounded by a radical function and other lines, about the In the next example, we will determine the volume generated by the revolution Thus, the volume of the solid of revolution is Thus, we have 𝑎 = 0 and 𝑏 = 3, and the volume of the solid of revolution is given by

The limits of the integral, 𝑎 and 𝑏, are determined by the vertical bounds of 𝑥 in the region bounded by the curves, 0 ≤ 𝑥 ≤ 3 this can also be visualized from the plot of the region bounded by the curves. The vertical cross-sectional shape of our solid will be a disk, and the radius, 𝑅, of each disk will be the value of the function at that point, 𝑅 = 𝑥 + 4. Since we rotated the region about the 𝑥-axis, the volume is given by

Washers and disk graph and shells