erplex
  • Lessons
  • Problems
  • Speed Run
  • Practice Tests
  • Skill Checklist
  • Review Videos
  • Landing Page
  • Sign Up
  • Login
  • erplex
    IB Math AASL
    /
    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.

    Integrals of sums and scalar products

    SL 5.5

    In the same way that constant multiples can pass through the derivative, they can pass through the integral:

    ∫af(x)dx=a∫f(x)dx🚫

    And in the same way that the derivative of a sum is the sum of the derivatives:

    ∫f(x)+g(x)dx=∫f(x)dx+∫g(x)dx🚫


    Combining these two rules:

    ∫af(x)+bg(x)dx=a∫f(x)dx+b∫g(x)dx🚫


    Example:

    Evaluate the integral ∫2x3−5x21​dx.


    ∫2x3−5x21​dx   ​=∫2x3−51​x−2dx=2∫x3dx−51​∫x−2dx=2⋅4x4​−51​⋅−1x−1​+C=21​x4+5x1​+C​

    Integrals of sums and scalar products

    SL 5.5

    In the same way that constant multiples can pass through the derivative, they can pass through the integral:

    ∫af(x)dx=a∫f(x)dx🚫

    And in the same way that the derivative of a sum is the sum of the derivatives:

    ∫f(x)+g(x)dx=∫f(x)dx+∫g(x)dx🚫


    Combining these two rules:

    ∫af(x)+bg(x)dx=a∫f(x)dx+b∫g(x)dx🚫


    Example:

    Evaluate the integral ∫2x3−5x21​dx.


    ∫2x3−5x21​dx   ​=∫2x3−51​x−2dx=2∫x3dx−51​∫x−2dx=2⋅4x4​−51​⋅−1x−1​+C=21​x4+5x1​+C​
    Definite integralsKinematicsHL