Search over 10,000 free study notes

First, find the centre of the circle. Since we know the equation of the circle, we know that the centre (-g,-f) comes from the part of the equation -12x-6y, where -12=2g and -6=2f. Therefore, to get the c...

y = 3x⁴-8x³-3dy/dx = (3 x 4)x³-(8 x 3)x² dy/dx = 12x³ - 24x²

The first step is deciding on the method of integration. For this integral it makes the most sense to use substitution.Let u = x² + 1Differentiate w.r.t x => du/dx = 2xRearrange for dx=> ...

Integrate by parts:u = ln(x) u' = 1/x v' = 1 v = xBy parts formula: uv - ∫u'v dx Therefore we have: xln(x) - ∫x1/x dx = xln(x) - ∫1 dx = xln(x) - x (+c)

First combine the x-parts of the equation: 4x - 2x = 2x Next move the "number parts" so they are all on the same side: 2x + 8 = 10 ---> 2x = 2 Then divide through by 2 to move the 2 from the...