Lesson 01 Appsof Integrals Mar17
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The document discusses calculating the volume of solids of revolution using integrals. It provides the formula for finding the volume of a solid rotated about the x-axis between x=a and x=b using a cross-sectional area function A(x). It then works through an example of finding the volume of a right circular cone of height 4 and base radius 1, and confirms the result matches the standard volume formula for a cone.
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Lesson 01 Appsof Integrals Mar17
- 2. y x a b
- 3. The volume of a solid between x = a and x = b having a crosssectional are A(x) at input x is: b V = A(x) dx a
- 4. Find the volume of a right circular cone with base radius 1 and height 4. 4 V = A(x) dx 0 0 x 4 2 x A(x) = 16
- 6. V = 1 r2 h 3 = 1 (1)2 4 3 = 4 3 Confirms value from previous screen