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1 x I Find the area of the region bounded by the curves y=sin"[:] , y = o, and x = 4 obtained by integrating with respect to y. Your work...

Four calculus questions???? Written format, not multiple choice.

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1 x I Find the area of the region bounded by the curves y=sin"[:] , y = o, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative. (10 points)

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2. Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 1, and x = 1 is revolved around the line y = -3. (10 points)

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3- The base of a solid in the xy-plane is the first-quadrant region bounded y = x and y = x2. Cross sections of the solid perpendicular to the x-axis are squares. What is the volume, in cubic units, of the solid? (10 points)

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4- Determine if the Mean Value Theorem for Integrals applies to the function f(x) = x3 - 9x on the interval [-1, 1]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem. (10 points)

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