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Mathematics

9th -

12thgrade

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Area and Volume (Calculus)

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15 questions

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  • 1. Multiple Choice
    30 seconds
    1 pt

    Select the formula for finding area under a curve bounded by the x axis.

     abf(x)dx\int_a^bf\left(x\right)dx  

     ab[f(x)g(x)] dx\int_a^b\left[f\left(x\right)-g\left(x\right)\right]\ dx  

     ab[f(x)]2dx\int_a^b\left[f\left(x\right)\right]^2dx  

     πabf(x)dx\pi\int_a^bf\left(x\right)dx  

  • 2. Multiple Choice
    30 seconds
    1 pt
    Image

    Find the integral for the area under the curve.

    62 2(x2 + 6x + 10) dx\int_{-6}^{-2}\ 2\left(x^2\ +\ 6x\ +\ 10\right)\ dx

    62 2(x2 + 6x + 10) dx\int_{-6}^{-2}\ -2\left(x^2\ +\ 6x\ +\ 10\right)\ dx

    62 (x2 + 6x + 10) dx\int_{-6}^{-2}\ \left(x^2\ +\ 6x\ +\ 10\right)\ dx

    62 4(x2 + 6x + 10) dx\int_{-6}^{-2}\ -4\left(x^2\ +\ 6x\ +\ 10\right)\ dx

  • 3. Multiple Choice
    30 seconds
    1 pt
    Image

    Find the integral that would find the area of the region enclosed by the curves.

    05[(x22+4x3)(x2+6x8)]dx\int_0^5\left[\left(-\frac{x^2}{2}+4x-3\right)-\left(-x^2+6x-8\right)\right]dx

    15[(x2+6x8)(x22+4x3)]dx\int_1^5\left[\left(-x^2+6x-8\right)-\left(-\frac{x^2}{2}+4x-3\right)\right]dx

    15[(x22+4x3)(x2+6x8)]dx\int_1^5\left[\left(-\frac{x^2}{2}+4x-3\right)-\left(-x^2+6x-8\right)\right]dx

    05[(x2+6x8)(x22+4x3)]dx\int_0^5\left[\left(-x^2+6x-8\right)-\left(-\frac{x^2}{2}+4x-3\right)\right]dx

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