etermine whether the following statements are true and give an explanation or counter example Complete...
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Calculus
etermine whether the following statements are true and give an explanation or counter example Complete parts a through d below f b a If the curve y f x on the interval a b is revolved about the y axis the area of the surface generated is f a O A False To obtain the surface area integral of f x when it is rotated about the y axis on a b the function y f x must be solved for x in terms of y This yields the function x g y Then the su f b 2ng y 1 g y dy assuming g y is positive on the interval f a f b f a OB area integral becomes 2n y 1 f y dy b True The surface area integral of f x when it is rotated about the x axis on a b is 2 x 1 f x dy To obtain the surface area of the function when it is rotated about the y axis change a limits of integration to f x evaluated at each endpoint and integrate with respect to y This is assuming f y is positive on the interval f a f b
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