resitting it this year to get an A*, as last year I got 95 in C3 but only 78 in C4 . Oh well, having done further maths C4 is bliss.. For instance last year I hated implicit differentiation, but now I see it as free marks; and after doing 3D vectors in FP3, the 2D vectors in C4 which I used to hate are actually quite relaxing xD
The Vectors in C4 are still 3D but we don't really worry about that.
I really hate C4 compared to C3, but I probably got 100 in C3 so I only need 80. I would like to get as high as possible but I'm taking a break today and I'll revise hard tomorrow.
(ii) Expand (1+x)^-3 and multiply it with the answer in i. Only multiply the parts which produce co-efficients of x^3 and below because that's what the question asks.
x=tanθ, therefore x^2 = (tanθ)^2 Also, dx=(secθ)^2 dθ (the differential of tanθ) So you then have the integral of (secθ)^2 dθ divided by (1+(tanθ)^2 )^2
Since 1+(tanθ)^2 = (secθ)^2, you're left with the integral of dθ / (secθ)^2 as you can do some cancelling of powers. This is equivalent to (cosθ)^2 dθFor the second part you just have to change the limits and use the double angle formula (cosθ)^2= (1+cos2θ) / 2