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Firstly, to find the stationary points of a curve you must differentiate the equation of the curve. To do this each x component is multiplied by its current power and then the power is decreased by one. A...

(2+5) x -6 = 42

Firstly, we need to find two numbers that multiply together to make -15 and sum together to make +2. We try a few numbers and find that the solution is -3 and 5, as -3 x 5 = -15 and -3 + 5 = 2.Next you in...

∫(cos² 2x *sin³ 2x)dx u = cos2x - u =(du/dx) = -2sin2x - differentiate u dx = du/(-2sin(2x)) - dx = -1/2 ∫cos²2x * sin²2x du - sub in dx-1/2 ∫u²(1-u<...

This equation has no real roots, as when we test the equation with the formula b² - 4ac, we get 2² -415 = 4 - 20 = -16. As this is negative we can be assured that this equat...