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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: 6
    40

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    Consider the function g defined by g(x)=2−4sin2x. The following graph shows the curve y=g(x) for 0<x<23π​.

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    The graph of y=g(x) intercepts the x-axis at a, b, c and d, as shown.

    1. Find the values of a,b,c and d.

      [6]

    In the diagram above, the region enclosed by the curve of y=g(x) and the x-axis between x=b and x=c is shaded.

    1. Show that the area of the shaded region is 34π​+2√3.

      [6]

    The diagram below shows a circle of radius r circumscribing a shape whose area is 34π​+2√3.

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    1. Find the value of r.

      [5]
    41

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    A particle X moves in a straight line. Its velocity, v feet per second, from the origin after t seconds is given by v(t)=3t2−12t+9.

    1. State the initial velocity of particle X.

      [1]
    2. Find the time(s) at which particle X changes directions.

      [3]

    The velocity of X reaches a minimum when t=q.

    1. Show that v(q)=−3.

      [2]

    Let a be the acceleration of particle X.

    1. Find a when t=q+1.

      [4]

    Particle X starts at the origin when t=0.

    1. Find the total distance travelled by the particle when t=q.

      [6]
    42

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    44

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