Taylor Series Question
Stuck on this question which involves Taylor series
I have a solution for this but don't understand it:
The solution involves denoting the integral by I(a) and then differentiating whats inside the integral while keeping x constant but i don't get why
i.e
I(a) = I(0) + I'(0)a + 1/2 I''(0)a^2… unitl a^5
where I'(a) = integral ( sin(acosx)sinx) so i'(0) = 0 etc.
I have a solution for this but don't understand it:
The solution involves denoting the integral by I(a) and then differentiating whats inside the integral while keeping x constant but i don't get why
i.e
I(a) = I(0) + I'(0)a + 1/2 I''(0)a^2… unitl a^5
where I'(a) = integral ( sin(acosx)sinx) so i'(0) = 0 etc.
Original post by Jammy4410
Stuck on this question which involves Taylor series
I have a solution for this but don't understand it:
The solution involves denoting the integral by I(a) and then differentiating whats inside the integral while keeping x constant but i don't get why
i.e
I(a) = I(0) + I'(0)a + 1/2 I''(0)a^2… unitl a^5
where I'(a) = integral ( sin(acosx)sinx) so i'(0) = 0 etc.
I have a solution for this but don't understand it:
The solution involves denoting the integral by I(a) and then differentiating whats inside the integral while keeping x constant but i don't get why
i.e
I(a) = I(0) + I'(0)a + 1/2 I''(0)a^2… unitl a^5
where I'(a) = integral ( sin(acosx)sinx) so i'(0) = 0 etc.
Do you want a solution?
Original post by Jammy4410
Stuck on this question which involves Taylor series
I have a solution for this but don't understand it:
The solution involves denoting the integral by I(a) and then differentiating whats inside the integral while keeping x constant but i don't get why
i.e
I(a) = I(0) + I'(0)a + 1/2 I''(0)a^2… unitl a^5
where I'(a) = integral ( sin(acosx)sinx) so i'(0) = 0 etc.
I have a solution for this but don't understand it:
The solution involves denoting the integral by I(a) and then differentiating whats inside the integral while keeping x constant but i don't get why
i.e
I(a) = I(0) + I'(0)a + 1/2 I''(0)a^2… unitl a^5
where I'(a) = integral ( sin(acosx)sinx) so i'(0) = 0 etc.
I haven't got time for a proper look now, but if alpha is much less than one what happens if you express the integrand as a Maclaurin series and integrate term by term?
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