calculus 2 help?

Find the exact area of the surface obtained by rotating the curve about the x-axis. 

(a) y = sqrt(7 − x), 1 ≤ x ≤ 7   

(b) y = sqrt(1+e^x), 0 ≤ x ≤ 6

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  • Pope
    Lv 7
    1 month ago

    The first actually plays better as a geometry problem than a calculus problem. The solid of revolution is a paraboloid. Its axis is the x-axis, its base radius is √(6), and its height is 6.

    volume = (1/2)π√(6)²(6) = 18π

  • david
    Lv 7
    1 month ago

    A = 2pi r X width

      . . . r = f(x)  . . . w = dx

     integral (from 1 to 7) [(2pi)(sqrt(7 − x))dx]

     =  (2pi) integral (from 1 to 7) [(sqrt(7 − x))dx]

     =  (2pi)[(-2/3)(7-x)^(3/2)]  <<<  evaluate from 1 to 7

     . . . you can do the last step

    I leave (b) for you to do .. you an do it .. just try

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