Search over 10,000 free study notes

There are 2 methods of solving this: completing the square or calculus, which makes this a versatile question for both GCSE and A Level students. It is also fairly simple to adapt.
Using calculus, th...

dy/dx = 4/(x^2+5) - 4x(2x)/(x^2+5)dy/dx= 4(5-x^2)/(x^2+5)^2Part B4(5-x^2)/(x^2+5)^2<05-x^2<05<x^2

First we need to use the factor theorem to find a factor.f(1)=-25 so x-1 is not a factorf(-1)=9 so x+1 is not a factorf(2)=0 so x-2 is a factorSo x-2 is our starting point, we need to polynomial division ...

Step 1 differentiate substitution: du/dx = -2sin(2x)Step 2 rearrange for dx: dx=du/-2sin(2x)Step 3 substitute: integral= ∫u²sin³(2x).du/-2sin(2x)Step 4 get the integral in terms of u...

 y=x(x−1)y= x^2-xdy/dx= 2x-1