cos^n(x)

OP

5CA2264E-2333-4D53-8D02-28319852FF5F.jpg.jpeg

i can't figure out what u would put in place of the 2, cos its a sequence that goes 1, 2, 2, 2, etc.

(edited 2 years ago)

Reply 2

mqb2766

21

Can you make it larger, its very blurred.
Also, what is the original question?

OP

OP

Original post by ligmaAss

the question is to find an expression for Rn (the area i have labelled at the beginning)

(edited 2 years ago)

Reply 5

OP

Original post by ligmaAss

the question is to find an expression for Rn (the area i have labelled at the beginning)

btw its only for integer positive n

Reply 6

mqb2766

21

Original post by ligmaAss

the question is to find an expression for Rn (the area i have labelled at the beginning)

Are you asked to use Euler to find an expression for cos^n(x) or are you expected to use integration by parts to get a recursive/reduction formula?

Reply 7

I think making a general expression about cosⁿ(x) is the wrong way to go - better to do one for the integral as a whole.
One trick I know of is to assign some value I to the integral, then do a substitution y = pi/2 - x and see where it takes you

Either that or a recurrence relation. But focusing on the integrand won't get you anywhere.

(edited 2 years ago)

Reply 8

OP

Original post by mqb2766

Are you asked to use Euler to find an expression for cos^n(x) or are you expected to use integration by parts to get a recursive/reduction formula?

it doesn't say

Reply 9

OP

Original post by Sinnoh

I think making a general expression about cosⁿ(x) is the wrong way to go - better to do one for the integral as a whole.
One trick I know of is to assign some value I to the integral, then do a substitution y = pi/2 - x and see where it takes you

Either that or a recurrence relation. But focusing on the integrand won't get you anywhere.

i'll try the subsitution, because i dont think the recurrence would work, because wouldn't it just go on forever

Reply 10

mqb2766

21

WHat have you covered in class. I suspect its the latter using a reduction formula based on integration by parts. A relative simple recursive solution is obtained.

(edited 2 years ago)

Reply 11

OP

Original post by mqb2766

WHat have you covered in class. I suspect its the latter using a reduction formula based on integration by parts.

i do further maths edexcel, so i've done ibp

Reply 12

Original post by ligmaAss

i'll try the subsitution, because i dont think the recurrence would work, because wouldn't it just go on forever

Well if you're able to get R_nin terms of R_n-2 then that's good enough, that's a general expression

Reply 13

OP

Original post by Sinnoh

Well if you're able to get R_nin terms of R_n-2 then that's good enough, that's a general expression

is there no way to generalise it further?

Reply 14

Original post by ligmaAss

is there no way to generalise it further?

If you were asked to evaluate it for, say, R = 15, that's all you'd need

Reply 15

OP

Original post by Sinnoh

If you were asked to evaluate it for, say, R = 15, that's all you'd need

but i mean, would my method not work? Or even just finding a general formula for cos^n(x), is that possible?

Reply 16