CalculusAdditional / Further Maths

Finding the constant of integration

Find a curve’s equation from its derivative and a point.

  • Integrate the derivative and include .
  • Substitute the coordinates of the given point into the integrated function.
  • Solve for and write the complete function.

Example 1

Find if the curve passes through .

Integrate the derivative.Substitute the given point.Solve for the constant.

Example 2

Find if the curve passes through .

Integrate the derivative.Substitute the given point.Solve for the constant.

Your turn

Question 1

Find if the curve passes through .

Check answer
Integrate the derivative.Substitute the given point.Solve for the constant.
Question 2

Find if the curve passes through .

Check answer
Integrate the derivative.Substitute the given point.Solve for the constant.
Question 3

Find if the curve passes through .

Check answer
Integrate the derivative.Substitute the given point.Solve for the constant.
Question 4

Find if the curve passes through .

Check answer
Integrate the derivative.Substitute the given point.Solve for the constant.
Question 5

Find if the curve passes through .

Check answer
Integrate the derivative.Substitute the given point.Solve for the constant.
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