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The general formula for integration by parts to integrate something of the form u * v' is: u * v - (integral)[ (u' * v) dx ]. Thus we first need to write x * sin(...
We use the following double angle formulae cos(2x) = cos^2(x) - sin^2 (x) and sin(2x) = 2sin(x)cos(x) to see that 2(sin^2(x)- cos^2(x)) + 6 sin(x) cos(x) = -2-(sin^2(x)+ cos^2(x)) + 3*2 sin(x) cos(x) = -2...
x2 - 4x -12 is a quadratic equation with a general formula. It can be factorised by into brackets and solved.By looking at the equation, the last term is negative so one number in the factorise...
When using proof by induction we most often prove a statement P for positive integers n. We think about the problem in a domino-toppling fashion. The first step is to write out P(n=1), so inserting 1 for ...
As the triangle in the question is a right angled triangle we can use Pythagoras Theorem , a2+b2=c2. c is the size of the longest size which is what we are looking for an...
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