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    Math help Cross-section

    The base of each solid below is the region in the xy-plane bounded by the x-axis, the graph x^(1/2) and the line x=3. Fine the volume of the solid. Each cross-section of S4 perpendicular to the y-axis is an isoscelesles right triangles with hypotenuse in the xy-plane

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    Quote Originally Posted by dj41490 View Post
    The base of each solid below is the region in the xy-plane bounded by the x-axis, the graph x^(1/2) and the line x=3. Fine the volume of the solid. Each cross-section of S4 perpendicular to the y-axis is an isoscelesles right triangles with hypotenuse in the xy-plane

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    V = \int_c^d A(y) \, dy

    area of an isosceles right triangle with hypotenuse length H, is

    A = \frac{H^2}{4}

    length of a representative hypotenuse perpendicular to the y-axis in the xy plane is ...

    H = 3 - y^2

    so ...

    V = \int_0^{\sqrt{3}} \frac{(3-y^2)^2}{4} \, dy
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    thank you very much
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