(1) Find the length of the curve: 2 (1 3 y (2) Find the length of...

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(1) Find the length of the curve: 2 (1 3 y (2) Find the length of the curve: 1 (1 + x)/, X = In(sin 2y), /8 y /6. (3) Find the area of the surface, obtained by rotating the curve below around the x-axis: 1 x 1 y = + 6 2x 0 x 1. 2 x 1. (4) (4pt) Set up integrals (do not evaluate) for the areas of surfaces of revolution, obtained by rotating the given curve around x-axis and around y-axis, using integration in each variable for both cases - a total of four integrals. Equation of the curve: y = arctan x, 0 x 1. (1) Find the length of the curve: 2 (1 3 y (2) Find the length of the curve: 1 (1 + x)/, X = In(sin 2y), /8 y /6. (3) Find the area of the surface, obtained by rotating the curve below around the x-axis: 1 x 1 y = + 6 2x 0 x 1. 2 x 1. (4) (4pt) Set up integrals (do not evaluate) for the areas of surfaces of revolution, obtained by rotating the given curve around x-axis and around y-axis, using integration in each variable for both cases - a total of four integrals. Equation of the curve: y = arctan x, 0 x 1.