Find the volume generated by revolving about the x-axis the regions bounded by the following graphs: y = sqrt 1+x x = 0 x = 10

Question

Find the volume generated by revolving about the x-axis the regions bounded by the following graphs: y = sqrt 1+x x = 0 x = 10

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Harper 2 weeks 2021-10-12T08:43:05+00:00 1 Answer 0

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    2021-10-12T08:44:05+00:00

    Answer:

    60 pi cubic units.

    Step-by-step explanation:

    Given that a region bounded by

    y = \sqrt{1+x}  \\x = 0\\ x = 10

    is revolved around x axis.

    To find the volume of generated solid

    we know that when a curve is rotated form x=a to x=b around x axis

    Volume V = \int_a^b \pi y^2 dx\\

    Substitute a=0 , b =10 and y^2 =1+x

    we have

    Volume = \int_0^{10} \pi (1+x) dx\\= \pi (x+\frac{x^2}{2)} \\=\pi(10+50)\\= 60\pi

    Hence volume would be 60 pi cubic units.

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