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The integration by parts rule looks like this: ∫ u * v' dx = u * v - ∫ ( v * u' ) dx Hence in this example, we want to make our u = x and v' = sinx So we now need to work out what u' and v are: u' = 1 which ...

We are looking for dy/dx, and in this question, the key rule to remember is the chain rule. Therefore the first thing to do is the easy step, take the 3 down and minus 1 from it, this will give 3(6x-13) 2 . ...

Using Vieta's formulas, which make the correspondence between the sums and products of the roots of a polynomial and its coefficients, we can deduce that a + b = (-8)/2 = -4, a b = 1/2 =0.5 and a^2 + b^2 = (...

A geometric series is a series with a constant ratio between successive terms.

An inverse function is a function that "reverses" another function. That is, if f is a function mapping x to y , then the inverse function of f maps y back to x . [1]