C4 - edexcel INTEGRATION! Watch

shohaib712
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Are we expected to know how to integrate a^x? And the proof for it?
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RDKGames
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(Original post by shohaib712)
Are we expected to know how to integrate a^x? And the proof for it?
Probably.

Have a go at it, it's nothing over A-Level maths level and there is a hint in your formula booklet that you can use:

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shohaib712
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(Original post by RDKGames)
Probably.

Have a go at it, it's nothing over A-Level maths level and there is a hint in your formula booklet that you can use:

Oh nice so if i ever have a question on it i can just refer to this and then use integration via substitution to get:
(1/lna)a^x + c?

when your integrating:
e^u (1/lna) du. You're alowed to remove the 1/ln1 outside the integral right? is it only when you have a multiple you can remove it to the other side?
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RDKGames
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(Original post by shohaib712)
Oh nice so if i ever have a question on it i can just refer to this and then use integration via substitution to get:
(1/lna)a^x + c?
Yep.

when your integrating:
e^u (1/lna) du. You're alowed to remove the 1/ln1 outside the integral right? is it only when you have a multiple you can remove it to the other side?
1/ln(a) can be moved outside, yes. Because it is a constant in this process of integration, whereas u is not.
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shohaib712
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(Original post by RDKGames)
Yep.



1/ln(a) can be moved outside, yes. Because it is a constant in this process of integration, whereas u is not.
what do you mean by constant? I thought only multiples can be removed eg. integrating 2/(ax+b) = remove 2 to outside the integral, work out 1/(ax+b), then multiply answer (1/a)ln(ax+b) by 2?
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nwmyname
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(Original post by shohaib712)
Are we expected to know how to integrate a^x? And the proof for it?
yes, to put it in short. The proof, not that I can think of.
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RDKGames
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(Original post by shohaib712)
what do you mean by constant? I thought only multiples can be removed eg. integrating 2/(ax+b) = remove 2 to outside the integral, work out 1/(ax+b), then multiply answer (1/a)ln(ax+b) by 2?
Multiple are constants, but we are not restricted to only multiples.
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shohaib712
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(Original post by RDKGames)
Multiple are constants, but we are not restricted to only multiples.
but what about something like: (e^x)(2^x) wouldnt 2^x classify as a constant as we are multiplying it to e^x?
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RDKGames
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(Original post by shohaib712)
but what about something like: (e^x)(2^x) wouldnt 2^x classify as a constant as we are multiplying it to e^x?
No because it's being raised to a variable.

Being able to recognise what's a constant and what's a variable is extremely important in integration as it is the difference between making your life easy, or hell.
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shohaib712
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(Original post by RDKGames)
No because it's being raised to a variable.

Being able to recognise what's a constant and what's a variable is extremely important in integration as it is the difference between making your life easy, or hell.
Okay so bassically any number being added/multiplied will count as a constant so it can be removed. But anything with a letter cannot?
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RDKGames
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(Original post by shohaib712)
Okay so bassically any number being added/multiplied will count as a constant so it can be removed. But anything with a letter cannot?
It's not that basic so your generalisation is not quite correct. Also 'anything with a letter' doesn't mean that that will be a variable. Clearly, in the example you've done, a is a letter but it's a constant.

In the process of integration, we take all the 'letters' other than the letter we are integrating with respect to as constants (unless they are functions of x, as then these are just expressions in terms of x in 'disguise'). Whether they can be removed entirely from the integral is an entirely different matter to deal with. I.e. integrating ax means that you can factor the a out of the integral, but integrating something like a^x means you cannot do that since the two aren't separable.
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shohaib712
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(Original post by RDKGames)
It's not that basic so your generalisation is not quite correct. Also 'anything with a letter' doesn't mean that that will be a variable. Clearly, in the example you've done, a is a letter but it's a constant.

In the process of integration, we take all the 'letters' other than the letter we are integrating with respect to as constants (unless they are functions of x, as then these are just expressions in terms of x in 'disguise'. Whether they can be removed entirely from the integral is an entirely different matter to deal with. I.e. integrating ax means that you can factor the a out of the integral, but integrating something like a^x means you cannot do that since the two aren't separable.
Oh I see so if it is seperable and will give the same answer (if not removed from the integration) then its considered a constant. So when we did ln(a) why are we allowed to remove it from the integral? wouldnt it need to be integrated as well?
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JammieDodger27
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(Original post by shohaib712)
Oh I see so if it is seperable and will give the same answer (if not removed from the integration) then its considered a constant. So when we did ln(a) why are we allowed to remove it from the integral? wouldnt it need to be integrated as well?
Given that a is a constant, ln(a) is a constant
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