CalculusAdditional / Further Maths

Finding an unknown integration limit

Form and solve an equation for a missing limit.

  • Replace the unknown upper limit by a variable in .
  • Set this expression equal to the given integral and solve.
  • Check the stated range of the limit; reject roots that do not satisfy it.

Example 1

Find , given .

Evaluate the integral using the unknown limit.Rearrange and factorise.Keep the root in the stated range.

Example 2

Find , given .

Evaluate the integral using the unknown limit.Rearrange and factorise.Keep the root in the stated range.

Your turn

Question 1

Find , given .

Check answer
Evaluate the integral using the unknown limit.Rearrange and factorise.Keep the root in the stated range.
Question 2

Find , given .

Check answer
Evaluate the integral using the unknown limit.Rearrange and factorise.Keep the root in the stated range.
Question 3

Find , given .

Check answer
Evaluate the integral using the unknown limit.Rearrange and factorise.Keep the root in the stated range.
Question 4

Find , given .

Check answer
Evaluate the integral using the unknown limit.Rearrange and factorise.Keep the root in the stated range.
Question 5

Find , given .

Check answer
Evaluate the integral using the unknown limit.Rearrange and factorise.Keep the root in the stated range.
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