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Initially, we must recognise the simplest way to integrate this equation is using the 'reverse chain rule' method. 

This means raising the value of the power, in this case '3', by one, and then div...

dy/dx = (4 * 3)x^(3-1) + 2x^(2-1)*cos(x²)

         = 12x² + 2xcos(x²) 

If the lines are parallel then when the line AB is given in the form y=mx+c then the gradient m of AB is equal to that of the other line. Rearranging the equation for line AB gives y=-(5/3)x-1 so m=-(5/3)...

For this example it would be better to use a dummy variable (a variable just to help with solving the equation but isn't a part of the final answer). Let us say our dummy variable, t = 1+x^2. So, substitu...

This is a common question in C4 and the trick used to solve it is often used in sub-sections to full questions.

To solve it, we must simplify the expression in terms of cos(2x) using two trigonomet...