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Further Mathematics
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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...

JH
4138 Views

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...

TG
2193 Views

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...

TG
3655 Views

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...

TR
33925 Views

Expand (2x+3)^4

We will you use Pascal's triangle in order to find coefficients:         1        1  1       1 2 1     1 3  3 1    1  4  6  4  1 so, our coefficients will be 1,4,6,4,1 now, let's expand: (2x+3)4

CP
3140 Views

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