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Question:Particle P of mass m and particle Q of mass km are moving in opposite directions on a smooth horizontal plane when they collide directly. Immediately before the collision the spe...

3x²-(1/4)x^-2+3
Split the problem into three separate terms and integrate independently.With any term where x is to the power of something, divide the coefficient by the value of...

The first thing to notice here is that the denominator of the integrand is a case of 'difference of two squares'. The integral, which I will call I, can be rewritten as the integral of 4/((1+x)(1-x)) dx. ...

Firstly we remind ourselves of the integration by parts formula. The formula used to integrate u dv/dx with respect to x = uv - the integral of v du/dx with respect to x.
So the first thing we have t...

The key fact here is to remember the relationship between the gradients of lines which are parallel and perpendicular. Two lines that are parallel will always have the same gradient. So if we have a line ...