Perplex
  • Lessons
  • Problems
  • Speed Run
  • Practice Tests
  • Skill Checklist
  • Review Videos
  • All Content
  • Landing Page
  • Sign Up
  • Login
  • Perplex
    IB Math AIHL
    /
    Integration
    /

    Video

    Video Reviews

    Watch comprehensive video reviews for most units, 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.

    Integration

    Video Reviews

    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.

    Definite integralsKinematicsHL

    The video will automatically pause when it reaches a problem.

    Volume of revolution about y-axis

    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

    V=∫ab​πx2dy📖


    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:

    1−2x=y2⇒x=21−y2​

    So the volume is

    V    ​=∫01​π(21−y2​)2dy =4π​∫01​1−2y2+y4dx=4π​(y−32​y3+5y5​)01​ =4π​(1−32​+51​)=152π​​

    Volume of revolution about y-axis

    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

    V=∫ab​πx2dy📖


    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:

    1−2x=y2⇒x=21−y2​

    So the volume is

    V    ​=∫01​π(21−y2​)2dy =4π​∫01​1−2y2+y4dx=4π​(y−32​y3+5y5​)01​ =4π​(1−32​+51​)=152π​​
    Definite integralsKinematicsHL