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# C1 Intergration watch

1. dy/dx = 5+ 1/x²

a)Use integration to find y in terms of x.²

b)Given that y = 7 when x = 1, find the value of y at x = 2.
2. a) y = 5x - 1/x + constant

b) constant = 3
When x = 2, y= 12.5
3. dy/dx = 5+ 1/x²

ok, rearrange it;

dy/dx = 5 + x^-2 (1/x^2 = x^-2)

then integrate;

5x - x^-1 + c where c is a constant

re-arrange

y = 5x - 1/x + c

and thats your equation

b.

you need to work out what c is;

sub in y = 7 and x = 1

7 = 5(1) - 1/1 + c

so

7 = 5 -1 + c

c = 3

then sub in x = 2

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Updated: February 1, 2006
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