6. Using the graph below as a guide, set up a definite integral for the area of the region bounded by the graphs of y = -3x^2 + 6x + 7 and y = x^3 - 12x^2 + 21x. Then evaluate the integral using the Fundamental Theorem of Calculus. (8) -3x^2 + 6x + 7 (1, 10) x^3 - 12x^2 + 21x (7, -98)
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To find the points of intersection, we need to solve the equation -3x^2 = x^3 - 12x^2. Rearranging the terms, we get x^3 - 9x^2 = 0. Factoring out x^2, we have x^2(x - 9) = 0. So, the points of intersection are x = 0 and x = 9. Show moreā¦
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