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Further Mathematics

A Level

How do you calculate the cross product of two vectors?

To calculate the cross product of two vectors you take the coordinates of vector 1 which are (x₁,y₁,z₁) and the coordinates of vector 2 which are (x₂,y₂

Answered by Michael K. • Further Mathematics tutor

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Find the area of the surface generated when the curve with equation y=cosh(x) is rotated through 2 pi radians about the x axis, with 2<=x<=6

Use the formula for the surface area of revolution, which requires dy/dx. So find dy/dx = sinh(x) and substitute dy/dx and y into the formula with the limits provided in the question (2 and 6). Then evalu...

Answered by Jakub H. • Further Mathematics tutor

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How do I know which substitution to use if I am integrating by substitution?

It is not just trial and error, as this will eat away time in the exam. if you can't see it straight away then you need to consider some things. for example a common question might be find the integral of...

Answered by Thomas G. • Further Mathematics tutor

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How do you find the derivative of arcsinx?

to find the derivative, we can first make this easier to visualise. Say a second variable, y, is included to make this become y = arcsinx. now if we sin both sides, we get siny = x. we already know the de...

Answered by Thomas G. • Further Mathematics tutor

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Show, using de Moivre's theorem, that sin 5x = 16 sin^(5) x - 20 sin^(3) x + 5 sin x

Using the question, first use de Moivre's theorem to say (cos x + i sin x)^5 = cos 5x + isin 5x. Now we can use a binomial expansion on the RHS to say

cos 5x + isin 5x = cos⁵ x + 5i cos...

Answered by Tom R. • Further Mathematics tutor

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