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    So I tried to do this integral and I got 16(cos^4x)/sinx
    I am guessing I'm very wrong. But I don't know why I'm wrong


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    (Original post by maths_4_life)
    So I tried to do this integral and I got 16(cos^4x)/sinx
    I am guessing I'm very wrong. But I don't know why I'm wrong


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    There's not a nice way to say this, but yeah, what did you try?
    I'd recommend writing \cos^3(x)=\cos(x)(1-\sin^2(x)) and then proceeding by inspection or a substitution.
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     \displaystyle \int \cos^3 x dx =\int \cos x (\cos^2 x ) dx = \int \cos x (1-\sin^2 x) dx = \int \left ( \cos x -\sin^2 x\cos x \right ) dx .
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    (Original post by joostan)
    There's not a nice way to say this, but yeah, what did you try?
    I'd recommend writing \cos^3(x)=\cos(x)(1-\sin^2(x)) and then proceeding by inspection or a substitution.
    This is what I did...why is it wrong?
    Name:  ImageUploadedByStudent Room1459283296.734679.jpg
Views: 178
Size:  111.7 KB
    I hope you can read it


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    (Original post by maths_4_life)
    So I tried to do this integral and I got 16(cos^4x)/sinx
    I am guessing I'm very wrong. But I don't know why I'm wrong


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    I know you've been taught that you add one to the power, divide by the new power and the divide by the derivative. But that's just plain incorrect. It only applies to integrands of the form (ax+b)^n. Anything else, that "rule" doesn't hold anymore and you need to be a whole lot more creative. Differentiation is easy (squeezing toothpaste out of the tube) and integration is hard (putting the toothpaste back into the tube), there are no straightforward rules for it. The above users have given a nice way to integrate this function.
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    (Original post by Zacken)
    Differentiation is easy (squeezing toothpaste out of the tube) and integration is hard (putting the toothpaste back into the tube)
    This analogy is perfect :eek:
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    (Original post by Zacken)
    I know you've been taught that you add one to the power, divide by the new power and the divide by the derivative. But that's just plain incorrect. It only applies to integrands of the form (ax+b)^n. Anything else, that "rule" doesn't hold anymore and you need to be a whole lot more creative. Differentiation is easy (squeezing toothpaste out of the tube) and integration is hard (putting the toothpaste back into the tube), there are no straightforward rules for it. The above users have given a nice way to integrate this function.
    Ohhhh thanks for that I thought the rule always applied. Hopefully I won't make the same mistake in future. The methods above do make sense I just wanted to see what was wrong with mine.


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    (Original post by Zacken)
    I know you've been taught that you add one to the power, divide by the new power and the divide by the derivative. But that's just plain incorrect. It only applies to integrands of the form (ax+b)^n. Anything else, that "rule" doesn't hold anymore and you need to be a whole lot more creative. Differentiation is easy (squeezing toothpaste out of the tube) and integration is hard (putting the toothpaste back into the tube), there are no straightforward rules for it. The above users have given a nice way to integrate this function.
    OP not attacking you in any way, don't worry.

    But I must say I feel like C4 int is taught so badly. This chapter is so much understanding and so little method compared to a lot of the maths at A level. I've seen quite a few teachers just show their students the methods (like the rote way you've described, Zain) neglecting to give equal attention to when/(even why) each will work
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    (Original post by maths_4_life)
    This is what I did...why is it wrong?
    Name:  ImageUploadedByStudent Room1459283296.734679.jpg
Views: 178
Size:  111.7 KB
    I hope you can read it


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    (Original post by maths_4_life)
    This is what I did...why is it wrong?
    Name:  ImageUploadedByStudent Room1459283296.734679.jpg
Views: 178
Size:  111.7 KB
    I hope you can read it


    Posted from TSR Mobile
    Because:
    -16\cos^4(x)=\displaystyle\int -64\cos^3(x)\sin(x) \ dx \not\Rightarrow-16 \dfrac{\cos^4(x)}{\sin(x)} = \displaystyle \int -64\cos^3(x) \ dx.
    The \sin(x) is a function of x so you can't pull it out of the integral like that.
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    (Original post by Zacken)
    I know you've been taught that you add one to the power, divide by the new power and the divide by the derivative. But that's just plain incorrect. It only applies to integrands of the form (ax+b)^n. Anything else, that "rule" doesn't hold anymore and you need to be a whole lot more creative. Differentiation is easy (squeezing toothpaste out of the tube) and integration is hard (putting the toothpaste back into the tube), there are no straightforward rules for it. The above users have given a nice way to integrate this function.
    Are you seriously only an a level student? You're a genius oh my god. I have no hope


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    (Original post by joostan)
    ...
    By the way, you only need to use \displaystyle once in a set of \LaTeX tags and it'll apply over the entire thing. :-)
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    (Original post by maths_4_life)
    Are you seriously only an a level student? You're a genius oh my god.


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    Ikr?
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    (Original post by Student403)
    OP not attacking you in any way, don't worry.

    But I must say I feel like C4 int is taught so badly. This chapter is so much understanding and so little method compared to a lot of the maths at A level. I've seen quite a few teachers just show their students the methods (like the rote way you've described, Zain) neglecting to give equal attention to when/(even why) each will work
    Yea it's really frustrating. I want to know why things work for a start but I think the teachers can't even explain it. Also it hardly makes them look good because if I hadn't asked you guys/tried this question I could have got something like this wrong in an exam.


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    (Original post by maths_4_life)
    Are you seriously only an a level student?
    :yes:

    You're a genius oh my god. I have no hope
    Flattering but very untrue. :lol:

    Spoiler:
    Show
    It's very admirable that you're asking questions on here! You're not the type of person to go "oh well, doesn't work, lel" and instead want to find out why what you did was wrong instead of just accepting the new method. I guarantee that this will get you very far in any mathematical field and I'm entirely sure that you'll ace your exams.
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    (Original post by maths_4_life)
    Yea it's really frustrating. I want to know why things work for a start but I think the teachers can't even explain it. Also it hardly makes them look good because if I hadn't asked you guys/tried this question I could have got something like this wrong in an exam.


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    That's the key though. You asked and that makes you a really good learner. So keep using TSR (maths forum - stay away from chat :afraid:) and you'll be fine! :awesome:
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    (Original post by Zacken)
    By the way, you only need to use \displaystyle once in a set of \LaTeX tags and it'll apply over the entire thing. :-)
    Yes, I was having something of a mare as maybe you saw, was trying to find the error, so had split it up into two blocks of TeX, of course it was an excess bracket as usual -_-
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    (Original post by Student403)
    OP not attacking you in any way, don't worry.

    But I must say I feel like C4 int is taught so badly. This chapter is so much understanding and so little method compared to a lot of the maths at A level. I've seen quite a few teachers just show their students the methods (like the rote way you've described, Zain) neglecting to give equal attention to when/(even why) each will work
    Why can't you? Thank you though


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    (Original post by Student403)
    OP not attacking you in any way, don't worry.

    But I must say I feel like C4 int is taught so badly. This chapter is so much understanding and so little method compared to a lot of the maths at A level. I've seen quite a few teachers just show their students the methods (like the rote way you've described, Zain) neglecting to give equal attention to when/(even why) each will work
    Sorry wrong person


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    (Original post by joostan)
    Because:
    -16\cos^4(x)=\displaystyle\int -64\cos^3(x)\sin(x) \ dx \not\Rightarrow-16 \dfrac{\cos^4(x)}{\sin(x)} = \displaystyle \int -64\cos^3(x) \ dx.
    The \sin(x) is a function of x so you can't pull it out of the integral like that.
    Why can't you? Thanks though


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    (Original post by joostan)
    Yes, I was having something of a mare as maybe you saw, was trying to find the error, so had split it up into two blocks of TeX, of course it was an excess bracket as usual -_-
    That and accidentally using a square bracket instead of a curly one... seriously TeX, seriously?
 
 
 
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