Centre of mass by integration

Centre of mass by integration Quiz

Spec ME3–ME4 · AQA A-Level Further Maths: Quiz

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  1. 1. Find xˉ\bar{x} for the lamina under y=xy=x from x=0x=0 to x=3x=3.

    • A. 1.51.5
    • B. 22
    • C. 2.252.25
    • D. 33

  2. 2. Which expression gives yˉ\bar{y} for a lamina under y=f(x)y=f(x)?

    • A. ∫xy dx∫y dx\frac{\int xy\,dx}{\int y\,dx}
    • B. ∫y2 dx∫y dx\frac{\int y^2\,dx}{\int y\,dx}
    • C. ∫12x2 dx∫y dx\frac{\int \frac12x^2\,dx}{\int y\,dx}
    • D. ∫12y2 dx∫y dx\frac{\int \frac12y^2\,dx}{\int y\,dx}

  3. 3. Which expression gives xˉ\bar{x} for the solid formed by rotating y=f(x)y=f(x) about the xx-axis?

    • A. ∫xy2 dx∫y2 dx\frac{\int xy^2\,dx}{\int y^2\,dx}
    • B. ∫xy dx∫y dx\frac{\int xy\,dx}{\int y\,dx}
    • C. ∫x2y dx∫y dx\frac{\int x^2y\,dx}{\int y\,dx}
    • D. ∫πy2 dx∫xy dx\frac{\int \pi y^2\,dx}{\int xy\,dx}

  4. 4. Find xˉ\bar{x} for the lamina under y=x2y=x^2 from x=0x=0 to x=3x=3.

    • A. 1.51.5
    • B. 2.72.7
    • C. 2.252.25
    • D. 3.03.0

  5. 5. The region under y=xy=x from 00 to 44 is rotated about the xx-axis. Find xˉ\bar{x} of the solid.

    • A. 2.02.0
    • B. 3.03.0
    • C. 2.672.67
    • D. 1.331.33

Quiz