Let r be the shaded region in the first quadrant enclosed by the y-axis and the graphs of y=sinx and y=cosx.

a) find the area of r
b)find the volume of the solid generated when r is revolved about the x-axis
c)find the volume of the solid whose base is r and whose cross sections cut by planes perpendicular to the x-axis are squares

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step-by-step explanation:

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1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.