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Firstly, we note that a 'root' is simply a solution of the equation (at least, in this case). Let's start from what we've been told: x = 1/2 is a root of the equation. Since it's a solution, let's sub it ...

a) ask student: purpose of differentiation (i), how to perform differentiation (ii) (i) to find the gradient of a curve (ii) multiply the coefficient of x by its indice then minus one from the indici perf...

Recall that ∫uv'=uv- ∫u'v Set u=sin²(x), v'=1 Therefore u'=2sin(x)cos(x) and v=x which gives us the following:

∫sin²(x)dx = xsin²(x) - ∫2xsin(x)cos(x)dx

The second integral in the above expr...

1 x 10^-9

we start  y factoring and solving for each equation:

cos(x) (2cos(x) - 1) = 0 

this means: 

cos(x) = 0 and cos(x) = 1/2

from the first equation we get:   x = 90

and from...