# A level integration help pls!!

#1
If i were to integrate (sinx)^4 using reverse chain rule, would that make 1/4cosx (sinx)^3?
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3 months ago
#2
No. Also cant see a way to integrate that directly using the reverse chain rule.
Last edited by mqb2766; 3 months ago
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3 months ago
#3
(Original post by Immaculatevibes)
If i were to integrate (sinx)^4 using reverse chain rule, would that make 1/4cosx (sinx)^3?
Have you tried differentiating that? You don't get back to (sin x)^4
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#4
(Original post by mqb2766)
No. Also cant see a way to integrate that using the reverse chain rule.
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#5
(Original post by Muttley79)
Have you tried differentiating that? You don't get back to (sin x)^4
Sorry i meant (sinx)^3 not 4. However, if i were to do it another way, can i use substitution instead?
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3 months ago
#6
(Original post by Immaculatevibes)
If the question doesnt provide any hints/indication, the usual way is to (identity) transform the trig power to a multiple angle (double, quadruple), then integrate that.

An alternative here could be to use a binomial type identity transformation and use the reverse chain rule on the individual terms.
Last edited by mqb2766; 3 months ago
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#7
(Original post by mqb2766)
If the question doesnt provide any hints/indication, the usual way is to (identity) transform the trig power to a multiple angle (double, quadruple), then integrate that.
Ohh okay, im not sure what you mean by multiple angle? I haven’t learnt that before (if it helps i am doing edexcel a level maths)
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3 months ago
#8
(Original post by Immaculatevibes)
Ohh okay, im not sure what you mean by multiple angle? I haven’t learnt that before (if it helps i am doing edexcel a level maths)
Can you upload the full question?
You have met mutiple angles, so
cos^2(x) = (cos(2x) + 1)/2
for instance
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#9
(Original post by mqb2766)
Can you upload the full question?
You have met mutiple angles, so
cos^2(x) = (cos(2x) + 1)/2
for instance
I found the question online, so it only asks us to integrate (sinx)^3 (there isn’t any other info)

Ohh i don’t think I’ve seen that before, do you know which sub-chapter it is in the edexcel book?
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3 months ago
#10
(Original post by Immaculatevibes)
Sorry i meant (sinx)^3 not 4. However, if i were to do it another way, can i use substitution instead?
No - your teacher should have gone over how to tackle powers of sin [and cos and tan].
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3 months ago
#11
(Original post by Immaculatevibes)
I found the question online, so it only asks us to integrate (sinx)^3 (there isn’t any other info)

Ohh i don’t think I’ve seen that before, do you know which sub-chapter it is in the edexcel book?
Trig identities? Theyre commonly used for integration problems so there will be examples in the integration section as well. Note your problem is now a cubic but was originally a quartic.
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#12
Ohh guys i think i know where i went wrong, when i was searching for how to do it, everyone is using substitution. So they’d split sin^3x into (1-cos^2x)(sinx) and then they’d integrate from there
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3 months ago
#13
(Original post by Immaculatevibes)
Ohh guys i think i know where i went wrong, when i was searching for how to do it, everyone is using substitution. So they’d split sin^3x into (1-cos^2x)(sinx) and then they’d integrate from there
One way to do it, yes.
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#14
(Original post by mqb2766)
Trig identities? Theyre commonly used for integration problems so there will be examples in the integration section as well. Note your problem is now a cubic but was originally a quartic.
Yes sorry, i used misread the question. I meant sin^3x not sin^4x. So would i just use trig identities to integrate it?
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3 months ago
#15
(Original post by Immaculatevibes)
Yes sorry, i used misread the question. I meant sin^3x not sin^4x. So would i just use trig identities to integrate it?
Its certainly something to try.
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#16
(Original post by mqb2766)
One way to do it, yes.
Thank you so much for your help. Ahah i just realised that i need to do more practice on this topic because im getting confused. Thanks again!
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#17
(Original post by Muttley79)
No - your teacher should have gone over how to tackle powers of sin [and cos and tan].
Turns out i got confused! Mqb2766 has helped me realise that I need to go over trig stuff because my teacher did go over it but i still didn’t get it so now im going to do some practice on that part, thanks for the help though!
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3 months ago
#18
I've moved this to the maths forum.
You could try rewriting sin(3x) in terms of powers of sin(x) and work backwards but that's quite long-winded
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#19
(Original post by Sinnoh)
I've moved this to the maths forum.
You could try rewriting sin(3x) in terms of powers of sin(x) and work backwards but that's quite long-winded
Thank you! I will attempt the question and see where I get up to 😣
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