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y = x³ - 3x² - 24x + 5, First, calculate the derivative of y and find its roots when y = 0:dy/dx = 3x² - 6x -24 = 0 -> x² - 2x - 8 = 0 -> (x+2)(x-4) = 0Th...

512

Use the formula: ∫uv' dx = uv - ∫u'v dx (use I = the integral we're looking for)Note we cant integrate ln x easily but we can differentiate into 1/x so we use:u = ln x and v' = x we have u' = 1/x and v =...

y = 3x -2(3x-2)² - x - 6x² = 0 9x²- 12x + 4 - x - 6x² = 03x² - 13x + 4 = 0(3x - 1)(x-4) = 0 x = 1/3 or x = 4then y = -1 when x = 1/3 and y = 10 for...

Using V = pi* integral of y² between b and a with respect to x , where V is the volume of generated solid.y² = 2x + 1 Integrating between given limits yields a result of 3.75Multipl...