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C1 Integration Question

Edit: Complete

Find the equation of the curve with the given derivative of yy with respect to xx that passes through the given point:

dydx=(x+2)2\frac {dy}{dx} = (x+2)^2; point (1, 7)

(x+2)(x+2)=x2+4x+4(x+2)(x+2) = x^2 + 4x + 4

y=13x3+2x2+4x+cy = \frac {1}{3}x^3 + 2x^2 + 4x + c

7=13+2+4+c7 = \frac {1}{3} + 2 + 4 + c

7=13+63+123+c7 = \frac {1}{3} + \frac {6}{3} + \frac {12}{3} + c

7=193+c7 = \frac {19}{3} + c

213193=c\frac {21}{3} - \frac {19}{3} = c

c=23c = \frac {2}{3}

So, 13x3+2x2+4x+23\frac {1}{3}x^3 + 2x^2 + 4x + \frac {2}{3}
(edited 13 years ago)
Reply 1
sub in x=1 and set y = 7
Original post by joeh37

Original post by joeh37
sub in x=1 and set y = 7


This, and then solve for C.
Reply 3
Original post by im so academic
This, and then solve for C.


That was implied :tongue:
Original post by im so academic
This, and then solve for C.


7=13x3+2x2+4x+c7 = \frac {1}{3}x^3 + 2x^2 + 4x + c

So would that be:

7=13+2+4+c7 = \frac {1}{3} + 2 + 4 + c

Right?

But how would c = 23\frac {2}{3}?
(edited 13 years ago)
Original post by Mr Inquisitive

Original post by Mr Inquisitive
7=13x3=2x27 = {1}{3}x^3 = 2x^2

So would that be:

7=1+1+4+c7 = 1 + 1 + 4 + c

Right?

But how would c = 23\frac {2}{3}?


y = 1/3 + 2 + 4 + c

7 = 19/3 + c

Then rearrange to find c. (which is 2/3).

Substitute the value for c in f(x) to get the equation.
Original post by im so academic
y = 1/3 + 2 + 4 + c

7 = 19/3 + c

Then rearrange to find c.


Ahh, thank you. :smile:
Original post by Mr Inquisitive

Original post by Mr Inquisitive
Ahh, thank you. :smile:


Remember though that is not the answer as the question specifically states to write down the equation.
Hi GUYS IM MR INQUISITIVE AND

1 TIMES 2 = ...


... 1!!!???




What the ****.
Original post by im so academic
Remember though that is not the answer as the question specifically states to write down the equation.


Just the y=13x3+2x2+4x+23y = \frac{1}{3}x^3 + 2x^2 + 4x + \frac {2}{3} then?
Original post by Mr Inquisitive

Original post by Mr Inquisitive
Just the y=13x3+2x2+4x+23y = \frac{1}{3}x^3 + 2x^2 + 4x + \frac {2}{3} then?


:yep:
Original post by M Loy is God

Original post by M Loy is God
Hi GUYS IM MR INQUISITIVE AND

1 TIMES 2 = ...


... 1!!!???




What the ****.


Lol this. :p:
Original post by im so academic
Lol this. :p:


I hate typos. :frown:
Reply 13
sub in x=1 and y=7, rearrange to get C.

voila

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