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f^-1(x) is equivalent to the inverse of the function f(x). To solve the inverse of a function, a series of steps must be followed:
1) Write out the equation x = f(y)
T...

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...

This is an example of a question where you would use the product rule, where if y = uv then dy/dx = udv/dx + vdu/dx. In this case u = 2x and v = ln(x). So first of all we will differentiate 2x wh...