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Not your average video:
Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.
Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.
Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.
Integration
Watch comprehensive video reviews for Integration, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.
Not your average video:
Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.
Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.
Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.
Not your average video:
Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.
Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.
Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.
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AHL 5.16
The volume of the solid produced by revolving a curve 2π about the y-axis by finding x in terms of y and evaluating
Example
Find the volume of the solid produced when the curve y=√1−2x is revolved 2π about the x-axis.
First find the bounds by plugging in x=0 (this gives the y-intercept: y=1. Since √1−2x>0, the lower bound is zero.
Then find x in terms of y:
So the volume is
AHL 5.16
The volume of the solid produced by revolving a curve 2π about the y-axis by finding x in terms of y and evaluating
Example
Find the volume of the solid produced when the curve y=√1−2x is revolved 2π about the x-axis.
First find the bounds by plugging in x=0 (this gives the y-intercept: y=1. Since √1−2x>0, the lower bound is zero.
Then find x in terms of y:
So the volume is