Given f(x) = sin^2(x) and g(x) = sin^4(x) (give exact answersfor all parts): a) Plot the functions on the x-interval [0, ?].Find the volume when the region enclosed by the curve and thex-axis is rotated about the line x = ?. b) Find the area of theregion. 1?b Aa and y = 1? b 1(f(x)2 ?g(x)2)dx. Find thex-coordinate of the center of Aa2 mass of the region. In a printstatement, explain why this answer makes sense based on the graphin part a). d) When the region rotates about the line x = ?, howfar does the center of mass travel? Multiply this value by thearea. What do you notice when you compare your answer to parta)?
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