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integration c4 help

Can someone please help me at 1:15 of this video

http://www.examsolutions.net/a-level-maths-papers/worked-solution/worked-solution.php?paper_id=42&solution=8.3

he explains integrate y dx
now y is obvious but he says to get dx first of all what is dx and in the end why do we need it because it ends up being dt anyway i thought it was just something you stick at the end of integral or when diff any help would be great thanks !
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Avatar for Little Ant
Little Ant
Original post by Adl91
Can someone please help me at 1:15 of this video

http://www.examsolutions.net/a-level-maths-papers/worked-solution/worked-solution.php?paper_id=42&solution=8.3

he explains integrate y dx
now y is obvious but he says to get dx first of all what is dx and in the end why do we need it because it ends up being dt anyway i thought it was just something you stick at the end of integral or when diff any help would be great thanks !


Okay, I'll try to explain this but I may fail.

dx, in this case, means 'with respect to x'. As the curve is plotted as y against x and you're trying to find the area under a curve that is plotted on the y vs x plane, you're integrating y with respect to the variable x.

However, as you don't have any equation in which y a function of x, but instead you have y is a function of the parameter t, you need to integrate with respect to t (or work out the y vs x eqn). But as the area is with respect to x you need to transfer the integral so its all with respect to t.


As you know the relationship between x and t you can differentiate x to find dx/dt.

From here is just the chain rule, by putting (dx/dt)*dt you effectively have just dx but written in a form so that it is with respect to t so that you CAN integrate it.

NB: Remember to change the limits! :smile:

I hope this helped, I'm not terribly good at explaining things! C4 is fun! I took it in Jan!
(edited 11 years ago)
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Avatar for Adl91
Adl91
OP
1
thanks man decided to leave c4 and start m1 tho and already confused with a simple concept :frown: have a look at my post if u could give me a hand would save my life right now !

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