In this video I go over another example on finding the volume of a shape formed by rotating a function about the x-axis. In this example I solve the volume of the shaper formed by rotating the function y = x^1/2 or y = sqrt(x) about the x-axis from x = 0 to 1.

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Integrals and Volumes: Example 2

Example:

Find the volume of the solid obtained by rotating about the x-axis the region under the curve y =x^1/2 from 0 to 1. Illustrate the definition of volume by sketching a typical approximating cylinder.

Solution:

Did we get a reasonable answer?? We can double check by considering the function y = 1 instead.

Thus in our example the volume is computed as half this cylinder's volume, which seems about right.