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Use integration by parts to find the integral of xsinx, with respect to x

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 ...
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Answered by Toby S. • Maths tutor
58966 Views

Differentiate y = (6x-13)^3 with respect to x

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 . ...
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Answered by Toby S. • Maths tutor
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Lisa, Max and Punita share £240 in the ratio 3 : 4 : 8 How much more money than Lisa does Punita get?

We should put the names aside to begin with and just look at the ratio and the price. In order to find out how much the ratio 3, the ratio 4 and the ratio 8 are worth, we need to find out how much the ratio ...
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Answered by Freddie R. • Maths tutor
20417 Views

The quadratic equation 2x^2 + 8x + 1 = 0 has roots a and b. Write down the value of a + b, a*b and a^2 + b^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 = (...
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Answered by Andreea I. • Maths tutor
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What is a geometric series?

A geometric series is a series with a constant ratio between successive terms.
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Answered by Ming Fung Y. • Maths tutor
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