IB DP Maths: AI HL复习笔记5.4.4 Volumes of Revolution
Volumes of Revolution Around x-axis
What is a volume of revolution around the x-axis?
- The volume of revolution is the volume of this solid
- Be careful – the ’front’ and ‘back’ of this solid are flat
- they were created from straight (vertical) lines
- 3D sketches can be misleading
How do I solve problems involving the volume of revolution around the x-axis?
Visualising the solid created is helpful
-
- Try sketching some functions and their solids of revolution to help
STEP 1
STEP 2
Use a GDC and the formula to evaluate the integral
Thus find the volume of revolution
Exam Tip
- Functions involved can be quite complicated so type them into your GDC carefully
- Whether a diagram is given or not, using your GDC to plot the curve, limits, etc (where possible) can help you to visualise and make progress with problems
Worked Example
Volumes of Revolution Around y-axis
What is a volume of revolution around the y-axis?
How do I solve problems involving the volume of revolution around y-axis?
- Use the formula
Exam Tip
- Functions involved can be quite complicated so type them into your GDC carefully
- Whether a diagram is given or not, using your GDC to plot the curve, limits, etc (where possible) can help you to visualise and make progress with problems
Worked Example
转载自savemyexam
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