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

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

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

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)

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)

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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