CalculusAdditional / Further Maths

Integration using a given derivative

Use a given derivative to evaluate a related integral.

  • A known derivative can reveal an antiderivative of a more complicated expression.
  • If , then for .
  • Compare the whole integrand with the given derivative, including any constant factor.

Example 1

Given , evaluate the integral.

Compare with the given derivative.Divide the known antiderivative by the same factor.

Example 2

Given , evaluate the integral.

Compare with the given derivative.Divide the known antiderivative by the same factor.

Your turn

Question 1

Given , evaluate the integral.

Check answer
Compare with the given derivative.Divide the known antiderivative by the same factor.
Question 2

Given , evaluate the integral.

Check answer
Compare with the given derivative.Divide the known antiderivative by the same factor.
Question 3

Given , evaluate the integral.

Check answer
Compare with the given derivative.Divide the known antiderivative by the same factor.
Question 4

Given , evaluate the integral.

Check answer
Compare with the given derivative.Divide the known antiderivative by the same factor.
Question 5

Given , evaluate the integral.

Check answer
Compare with the given derivative.Divide the known antiderivative by the same factor.
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