Carmens painting wins second prize in the contest. the painting that wins first prize has an area that is 3.2 times smaller than the greatest area the rules allow. what is the area of the first prize painting?

Find the volume of the solid whose base is the region bounded by f(x), g(x) and the x-axis on the interval [0, 1], and whose cross-sections perpendicular to the y-axis are squares. your work must show the integral, but you may use your calculator to evaluate it. give 3 decimal places for your answe