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  • Perplex
    IB Math AISL
    /
    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: 6
    12

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    On a hot summer afternoon, engineers study how heat distributes along a new metal alloy rod. Let T(x) be the temperature in °C at a point x  cm from one end of the rod, where 0≤x≤2. The temperature gradient satisfies

    dxdT​=6x

    and it is observed T(2)=10.

    1. Find T(x).

      [2]
    2. Find the average temperature Tˉ along the rod from x=0 to x=2.

      [2]
    13

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    EcoTech Ltd. tracks its annual profit. Let P(t) (in thousands of dollars) be its profit t years after founding. The rate of change of profit is modeled by

    dtdP​=3t2−10t,t≥0
    1. Determine whether the profit is increasing or decreasing when t=2.

      [2]
    2. Given that one year after founding the annual profit was $2,000, find an expression for P(t) for when t≥0.

      [3]
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