Search over 10,000 free study notes

STEP 1 Cannot integrate directly in this form, therefore use a trigonometric identity. Identity: sin(A) + sin(B) = 2sin((A+B)/2)cos((A-B)/2) STEP 2 (A+B)/2 = 3x             A + B = 6x   (1) (A-B)/2 = 5x  ...

We can think of the constant term in a function in terms of x, for example in x^2 + 3x + 2 as 2 being multiplied by x^0. Anything to the power of 0 is equal to one, so in our example we would have 2 * x^ ...

We can break this down into steps, going deeper each time. First we might just say: well, since integration is fundamentally the inverse process of differentiation and we know that the derivative of ln(x)...

Stationary points are points at which the gradient of the curve is zero. The gradient is given by dy/dx so we start by computing this using product rule to give us dy/dx=-sin²x+cos²x...

There are two stages to this integral. Stage 1: Notice that there is a quadratic inside a square root in the denominator. We wish to look for a substitution which will reduce this problem...