# integration help!

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Hljones17

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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

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

(Original post by

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

**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

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

**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

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RDKGames

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#4

**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

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Hljones17

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#5

(Original post by

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.

**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.

Thank you so much!!

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AspiringUnderdog

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#6

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

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

**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

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Hljones17

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#8

**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

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

(Original post by

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?

**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?

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#10

(Original post by

Close but when you differentiate 4x and 3x what do you get?

**AspiringUnderdog**)Close but when you differentiate 4x and 3x what do you get?

4x=4

3x=3?

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#11

(Original post by

I'm confused why do I need to differentiate 4x and 3x now? Sorry I'm really bad at this

4x=4

3x=3?

**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?

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RDKGames

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#12

**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?

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 and .

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#13

(Original post by

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

**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

8x4^4/4

15e^4x/4

-3cos(3x)/3

How do I present this as an answer?

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#14

(Original post by

So is it

8x4^4/4

15e^4x/4

-3cos(3x)/3

How do I present this as an answer?

**Hljones17**)So is it

8x4^4/4

15e^4x/4

-3cos(3x)/3

How do I present this as an answer?

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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#15

(Original post by

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 and .

**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 and .

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#16

(Original post by

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.

**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.

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#17

(Original post by

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!!

**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!!

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