Volumes by Cross Sections

Volumes by Cross Sections can be setting a unit volume, \( \delta V \) of a cross section. Then establish an integration for evaluating the volume of the entire solid.

Worked Examples of Volumes by Cross Sections

The base of a solid is formed by the area bounded by \( y = \cos x\) and \( y = -\cos x \) for \( \displaystyle 0 \le x \le \frac{\pi}{2} \). Vertical cross sections of the solid taken parallel to the \(y\)-axis are in the shape of isosceles triangles with the equal sides of length 1 unit. Find the volume of the solid.

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