Let R be the shaded region in the first quadrant enclosed

| August 30, 2017

Question
2) Let R be the shaded region in the first quadrant enclosed by the y-axis and the graphs of y=1-x^2 and y=sin(x^2), as shown in the figure to the left.

a) Find the area of R.

b) A horizontal line, y=k, is drawn through the point where the graphs of y=1-x^3 and y=sin(x^2) intersect. Find k and determine if this line divides R into two regions of equal area. Show the work that leads to your conclusion.

c) Find the volume of the solid generated when R is revolved around the line y=-3.

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