Page 43 - Math SL HB Sem 2
P. 43
BOUNDARY CONDITIONS ( SOLWNG FOR CONSTANT,C)
From the families of curves, we find that there is more than one curve when we find the
indefinite integral. This is because each curve has the same gradient. To determine which
of these curves is the one that we actually require, we must be provided with some extra
information. [1 this case we would need to be given the coordinates of a point on the
cuwe.
Example 12: Find the value ofthe constant ofthe integration if the curve whose derivative
is 2x and passes through the point(2 ,9). Ans: c:5
Example 13: Find the equation of the curve that has a second derivative y" = 4* *U *"
4 slope of 10 at the point ( 2 , 9 ). Ans: 3v = 2x3 + ll
