1322e-20191-notes03-filled.pdf - MAT1322 C ALCULUS II E...

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MAT1322 CALCULUSIIELIZABETHMALTAIS3. VolumesWe’ve now seen how definite integrals give us a way to compute areas of “weird”shapes bounded by functions.Let’s generalize these concepts to help us find volumes of 3-dimensional shapes.VOLUMESConsider a solid object that lies betweenx=aandx=b. What is its volume?solidApproximatevolumeusingslices.pl#n8E..q.,¥⇐€E€¥E¥⇐E€EE÷÷¥¥¥÷¥¥÷E÷EE÷¥÷€EE÷E31
Example 3.1.Find the volume of the solid obtained by rotating about thex-axis the region

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