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  • Perplex
    IB Math AIHL
    /
    Integration
    /

    Problems

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    Problem Bank - Integration

    Access custom-built, exam-style problems for integration. Each problem has a full solution and mark-scheme, as well as AI grading and support.

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    IB: 5
    17

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    The function f(x) has the definite integral ∫14​f(x)dx=6.

    1. Write down the value of ∫14​3f(x)dx

      [1]
    2. Find the value of ∫01.5​2f(2x+1)−3dx

      [5]
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    1. Evaluate the integral ∫√3x+1​dx

      [3]
    2. Hence find the value of ∫18​√3x+1​dx

      [3]
    19

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    The velocity, vms−1, of a particle moving in a straight line is given by v(t)=(3−t)cost, for 0≤t≤6 seconds. The following diagram shows the graph of v as a function of t.


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    Let t=q be the third time at which the particle changes direction.

    1. Show that q=23π​.

      [3]
    2. Find the distance travelled by the particle when t=q.

      [2]
    3. Find the acceleration of the particle when t=4.

      [2]
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