L10 - Volume Calculation by the Method of Slicing

L10 - Volume Calculation by the Method of Slicing - Volume...

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Volume By Slicing (Section 6.1) We used definite integrals to compute areas by making slices (rectangles) and adding up the areas of the slices. For volumes we will slice the solid into pieces whose volume can be approximated and then added together. Recall: Volume = So, as long as we know the __________ of the base of a region, we can find the volume by the equation ___________________. DEF The volume of a solid of known integrable cross-sectional area A(x) from x=a to x=b is the integral of A from a to b , __________________________ NOTE: Always integrate along the axis perpendicular to a slice. Steps to Calculate the Volume of a Solid: 1. Sketch the solid and a typical cross-section 2. Find a formula for A(x) , the area of a typical cross-section. 3. Find the limits of integration 4. Integrate A(x) using the FTC (part 2).
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Ex. A solid has slices perpendicular to the y-axis that are squares with one edge in the xy plane. The intersection of the solid with the xy plane is the region between the curves x = y
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L10 - Volume Calculation by the Method of Slicing - Volume...

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