Top answers

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 (3...
TG
3058 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 deriv...
TG
4775 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 = cos 5 x + 5i cos 4 x sin x +10i 2 cos...
TR
37212 Views

Find the integrating factor of the following first order ODE: dx/dt = -2tx +t.

Firstly rearrange the differential equation to fit the form dx/dt +P(t)x = Q(t). The integrating factor is then found by using the formula: u = EXP(INTG(P(t))). We know that P(t) = 2t and so by integrating w...
AT
8557 Views

Using your knowledge of complex numbers, such as De Moivre's and Euler's formulae, verify the trigonometric identities for the double angle.

de Moivre's: (cos(x)+isin(x)) n =cos(nx)+isin(nx) set n=2 (cos(x)+isin(x)) 2 =cos 2 (x)+2isin(x)cos(x)-sin 2 (x), which, according to de Moivre's cos 2 (x)+2isin(x)cos(x)-sin 2 (x)=cos(2x)+isin(2x) We notice...
CP
4945 Views