Question

Let R be the region in the first quadrant bounded by the x-axis and the graphs of y = in(x) and y=5-x, as shown in the figure above.


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 Let R be the region in the first quadrant bounded by the x-axis and the graphs of y = in(x) and y=5-x, as shown in the figure above.

 a) Find the area of R.

 b) Region R is the base of a solid. For the solid, each cross-section perpendicular to the x-axis is a right isosceles triangle whose leg falls in the region. Write, but do not evaluate, an expression involving one or more integrals that gives the volume of the solid.

 c) The horizontal line y = k divides R into two regions of equal area. Write, but do not solve, an equation involving one or more integrals whose solution gives the value of k.


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Let R be the region in the first quadrant bounded by the x-axis and the graphs of y = in(x) and y=5-x, as shown in the figure above.
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