integration help!

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Hljones17
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#1
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#1
Can anyone help answer this question I think it's asking me to intergrate

Find an expression for the area under the curve y=8x^3+15e^4x-3sin(3x)

We are really struggling with this
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yusyus
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#2
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#2
(Original post by Hljones17)
Can anyone help answer this question I think it's asking me to intergrate

Find an expression for the area under the curve y=8x^3+15e^4x-3sin(3x)

We are really struggling with this
you can seperate out the integrals,

so
int(8x^3)+int(15e^4x)-int(3sin(3x))
and do it step by step
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AspiringUnderdog
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#3
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#3
(Original post by Hljones17)
Can anyone help answer this question I think it's asking me to intergrate

Find an expression for the area under the curve y=8x^3+15e^4x-3sin(3x)

We are really struggling with this
Yeah you just need to integrate to find the expression. Do you know how do you that or would you like me to explain? Take it as three separate integrals if that helps.
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RDKGames
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#4
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#4
(Original post by Hljones17)
Can anyone help answer this question I think it's asking me to intergrate

Find an expression for the area under the curve y=8x^3+15e^4x-3sin(3x)

We are really struggling with this
Area between which two values?? Just integrate each term separately between the two values and add them up
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Hljones17
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#5
(Original post by AspiringUnderdog)
Yeah you just need to integrate to find the expression. Do you know how do you that or would you like me to explain? Take it as three separate integrals if that helps.
Would you mind explaining how do do this please?

Thank you so much!!
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AspiringUnderdog
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(Original post by Hljones17)
Would you mind explaining how do do this please?

Thank you so much!!
Okay so you know for 8x^3 you add one to the power and divide by this new number.

For integrating e^f(x) you get e^f(x)/f'(x)
Basically you divide e by the derivative of the power of e.

When integrating sinx you get -cosx but we have sin3x instead. Sin(f(x)) integrates to - cos(f(x))/f'(x).
Essentially meaning that you divide cos3x by the differential of 3x in this case.

Don't forget to include the coefficients of e and sin when doing this and you should be fine!

Let me know if you still need help
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Notnek
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#7
(Original post by AspiringUnderdog)
Okay so you know for 8x^3 you add one to the power and divide by this new number.

For integrating e^f(x) you get e^f(x)/f'(x)
Basically you divide e by the derivative of the power of e.

When integrating sinx you get -cosx but we have sin3x instead. Sin(f(x)) integrates to - cos(f(x))/f'(x).
Essentially meaning that you divide cos3x by the differential of 3x in this case.

Don't forget to include the coefficients of e and sin when doing this and you should be fine!

Let me know if you still need help
It’s worth mentioning that the integral rules that you’ve mentioned are only true when f(x) is linear.
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Hljones17
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#8
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(Original post by AspiringUnderdog)
Okay so you know for 8x^3 you add one to the power and divide by this new number.

For integrating e^f(x) you get e^f(x)/f'(x)
Basically you divide e by the derivative of the power of e.

When integrating sinx you get -cosx but we have sin3x instead. Sin(f(x)) integrates to - cos(f(x))/f'(x).
Essentially meaning that you divide cos3x by the differential of 3x in this case.

Don't forget to include the coefficients of e and sin when doing this and you should be fine!

Let me know if you still need help
So using your method I've integrated

8x^3 to 8x^4/4

15e^4x = 15e^4x/4x

3sin (3x) to - 3cos (3x)/3x

Is this right?
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AspiringUnderdog
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#9
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#9
(Original post by Hljones17)
So using your method I've integrated

8x^3 to 8x^4/4

15e^4x = 15e^4x/4x

3sin (3x) to - 3cos (3x)/3x

Is this right?
Close but when you differentiate 4x and 3x what do you get?
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Hljones17
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#10
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#10
(Original post by AspiringUnderdog)
Close but when you differentiate 4x and 3x what do you get?
I'm confused why do I need to differentiate 4x and 3x now? Sorry I'm really bad at this

4x=4

3x=3?
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AspiringUnderdog
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#11
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#11
(Original post by Hljones17)
I'm confused why do I need to differentiate 4x and 3x now? Sorry I'm really bad at this

4x=4

3x=3?
I don't entirely know how to explain it but that's how it is. For e to any power you divide by the derivative of the power and for trig function you divide by the derivative of what's in the bracket
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RDKGames
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#12
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#12
(Original post by Hljones17)
I'm confused why do I need to differentiate 4x and 3x now? Sorry I'm really bad at this

4x=4

3x=3?
TBH, not to come across in a rude manner, but you need to go back to the theory behind these in your textbook or ask your teacher about how these are done (and why each step is what it is, ie why we need to care about derivative of 3x and 4x) because these are very standard textbook integration types of questions that should've been covered in a lesson before you'd be given a problem like this.

You may as well answer your own question of "Why do I need to differentiate 4x and 3x?" by simply considering integration by substitution on \displaystyle \int e^{4x}.dx and \displaystyle \int \sin(3x).dx.
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Hljones17
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#13
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#13
(Original post by AspiringUnderdog)
I don't entirely know how to explain it but that's how it is. For e to any power you divide by the derivative of the power and for trig function you divide by the derivative of what's in the bracket
So is it

8x4^4/4

15e^4x/4

-3cos(3x)/3

How do I present this as an answer?
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AspiringUnderdog
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#14
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#14
(Original post by Hljones17)
So is it

8x4^4/4

15e^4x/4

-3cos(3x)/3

How do I present this as an answer?
Yeah I'm pretty sure that that would be correct. Just make it one line with your three variables added together.

Also I do think that you should listen to what RDKGames has said because this should be one of the first things covered in C3 calculus.
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Hljones17
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#15
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#15
(Original post by RDKGames)
TBH, not to come across in a rude manner, but you need to go back to the theory behind these in your textbook or ask your teacher about how these are done (and why each step is what it is, ie why we need to care about derivative of 3x and 4x) because these are very standard textbook integration types of questions that should've been covered in a lesson before you'd be given a problem like this.

You may as well answer your own question of "Why do I need to differentiate 4x and 3x?" by simply considering integration by substitution on \displaystyle \int e^{4x}.dx and \displaystyle \int \sin(3x).dx.
Yeah I will go back and look at the theory I like doing it once I know the answer. The problem is it's my partner he's started an engineering apprenticeship late so he's about 3 months behind and he walked in the first day and these are the kind of questions they were doing having already been through the theory in previous lessons. He's asked me to help with the maths as I did maths in college and he left school early but I've never seen anything like this (I only did maths at international Baccalaureate level) . I'm trying to get my head around it myself before explaining it to him lol. I've been having a look on GCSE bitesize but I will make sure I make sense of the theory before attempting to explain it to him. Thanks for your help!
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Hljones17
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#16
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#16
(Original post by AspiringUnderdog)
Yeah I'm pretty sure that that would be correct. Just make it one line with your three variables added together.

Also I do think that you should listen to what RDKGames has said because this should be one of the first things covered in C3 calculus.
Yeah now that I know the answer I'm going to go back and try to make more sense of how I got to the answer. Thank you for your help I really appreciate it!!
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AspiringUnderdog
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#17
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#17
(Original post by Hljones17)
Yeah now that I know the answer I'm going to go back and try to make more sense of how I got to the answer. Thank you for your help I really appreciate it!!
No problem xx
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