# Finding the Integrating constant 'C'

Evaluating the integrating constant C

Anti-differentiating then substituting in a known 'x' and 'y' value to determine the value of 'C'

Finding the original equation when given a derivative and point on the original function. Class Notes | Blank Notes Ex16.03

#### NuLake IES p104 to 105

Harder finding C

Practice finding 'C' from different situations - eg. given a gradient and a point Class Notes | Blank Notes

#### NuLake IES p106 to 107

The derivative of a constant is 0

eg. So the anti-derivative of 0 is any constant 'c'

or #### Mouse over box Which is the anti-derivative?

To find 'c' use a coordinate eg.(1,8) or value f(1)=8

Steps: 1) Anti-differentiate 2) Find 'c' 3) Solve for 'c' 4) Function #### Mouse over key words ###### Example:
 Find the equation for the graph of f(x) given that f'(x) = 6x2 + 8 and the graph of f(x) passes through the point (1,8) Steps: f'(x) = 6x2 + 8 1) Anti differentiate to find function f(x) f(x) = 2x3 + 8x + C 2) Substitute in x = 1 & y = 8 from the coordinate and rearrange to find 'C' f(x) = 2x3 + 8x + C 8 = 2x13 + 8x1 + C 8 = 2 + 8 + C 8 = 10 + C -2 = C 3) Write out the equation for f(x) f(x) = 2x3 + 8x + C f(x) = 2x3 + 8x - 2