find the volume V generated by rotating the region bounded by the given curves about the specified axis. y=17 sqrt(x), y=0, x=1; about x=-2?

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.

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  • Bryce
    Lv 7
    1 month ago

    V= 2π∫[0 to 1] (x + 2)17√x dx

    = 2π∫[0 to 1] 17x^(3/2) + 34x^(1/2) dx

    = 2π[(34/5)x^(5*/2) + (68/3)x^(3/2)]

    = 2π(34/5 + 68/3)= 2π*442/15= 884π/15≈ 185.1

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