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integration help(i think?)

1. The gradient of a curve is given by dy/dx=3x-4. Find the equation of the curve given that it passes through the point (3,1)

so integrate 3x-4 so= 3x^2/2-4x. can i get rid of the 2 on the denominator?
(edited 11 years ago)
Reply 1
Original post by dongonaeatu
1. The gradient of a curve is given by dy/dx=3x-4. Find the equation of the curve given that it passes through the point (3,1)

so integrate 3x-4 so= 3x^3/3-4x. can i get rid of the 3 on the denominator?


Where are you getting the 3 from?
Reply 2
To integrate you increase the power by one and divide by the new power. So yes you can cancel the 3 and would therefore have y=x^3-4x+d

Don't forget to include the constant!!!!

Solve using the values you know to find d.
Reply 3
Is your original expression supposed to be dy/dx = 3x - 4, i.e. the equationn of a straight line? If you've integrated incorrectly.

If it is supposed to be dy/dx = 3x^2 - 4, i.e. a quadratic, then yes, this gives you y = (3x^3)/3 - 4x + c. Of course you can cancel the 3s in the first term - it is just three times something divided by three.
Reply 4
Isn't it divided by two, not three :P


You divide by the new power bro

Also, +k on the end.
Reply 5
Original post by CD315
Where are you getting the 3 from?


sorry, i meant 2.

is the final answer for the equation of the curve y=3x^2/2-4x-1/2
(edited 11 years ago)
Reply 6
Original post by tamimi
Isn't it divided by two, not three :P


You divide by the new power bro

Also, +k on the end.


is the final answer for the equation of the curve y=3x^2/2-4x-1/2
Reply 7
That's what I make it.
Reply 8
Original post by dongonaeatu
is the final answer for the equation of the curve y=3x^2/2-4x-1/2


I believe it is :smile: Either that or we're both wrong.
Reply 9
Yep I seem to get -1/2. You don't need to get rid of the two, just sub in your x and y values after you've integrated. Best way just in case you make a mistake in getting rid of the 2.
Reply 10
Original post by mr tim
Yep I seem to get -1/2. You don't need to get rid of the two, just sub in your x and y values after you've integrated. Best way just in case you make a mistake in getting rid of the 2.


thanks tim, are you good at trigonometry?
Reply 11
Original post by dongonaeatu
thanks tim, are you good at trigonometry?


if you can tell me the question then I'll or someone else will tell you how to answer it.
Reply 12
Original post by mr tim
if you can tell me the question then I'll or someone else will tell you how to answer it.


http://www.thestudentroom.co.uk/showthread.php?t=1970260&p=37114590

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