IB DP Maths: AA HL復習筆記5.9.4 Advanced Applications of Integration
Area Between Curve & y-axis
What is meant by the area between a curve and the y-axis?
How do I find the area between a curve and the y-axis?
Exam Tip
Worked Example
Volumes of Revolution Around x-axis
What is a volume of revolution around the x-axis?
How do I solve problems involving the volume of revolution around x-axis?
Exam Tip
- If the given function involves a square root(s), problems can seem quite daunting
- However, this is often deliberate, as the square root will be squared when applying the Volume of Revolution formula, and should leave the integrand as something more manageable
- 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?
Exam Tip
- If the given function involves a square root, problems can seem quite daunting
- This is often deliberate, as the square root will be squared when applying the Volume of Revolution formula and the integrand will then become more manageable
- Whether a diagram is given or not, using your GDC to plot the curve, limits, etc (where possible) can help you to visualise the problem and make progress
Worked Example
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