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Mathematics LibreTexts

7E: Chapter Review Exercises

  • Page ID
    26048
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    Exercise \(\PageIndex{1}\)

    Sketch the regions and evaluate the integrals:

    1) \(\int_1^{\ln 8} \int_0^{\ln y} 2e^{x+y} \, dy dx\)

    2) \(\int_0^{2} \int_x^{2} 3y^2 sin({xy}) \, dy dx\)

    3) \(\int_0^{1} \int_0^{3} \frac{4x^2}{(y-1)^{2/3}} \, dy dx\)

    4) \(\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \frac{3}{(x^2+1)(y^2+1)} \, dy dx\)

    5) \(\int \int_{x^2+y^2 \leq 1} \ln (x^2+y^2)\, dA\)

    6) \(\int_0^2 \int_{y/2}^1 y e^{x^3} \,dx dy\)

    7) \(\int \int_Q \frac{dA}{(1+x^2)(1+y^2)}\), where \(Q\) is the first quadrant of the \(xy-\)plane.

    8) \(\int \int_R x \cos (y) \,dA\), where \(R\) is the region bounded by the coordinate axes and the curve \(y=1-x^2.\)

    Answer

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