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Area L

By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?

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Integral Equation

Solve this integral equation.

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Integral Sandwich

Generalise this inequality involving integrals.

Weekly Challenge 45: Integral Arranging

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2
There is no particular 'answer' to this question, but here are some points to consider:
  • Are there some that you know the answer to, others that you don't?
  • Are some equivalent under a change of variables?
  • Are some valid over different ranges of integration?
  • Are some larger than others over different ranges?
  • Are some more complex than others to evaluate?
  • Do some seem to have the same 'class' of answer?