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FP2 (MEI) Calculus 2: Integration using the inverse trigonometric functions

FP2 (MEI) Calculus 2: Integration using the inverse trigonometric functions. Let Maths take you Further…. Integration using the inverse trigonometric functions. Before you start… You need to be familiar with the laws of indices (Core 1 chapter 5) and logarithms (Core 2 chapter 11).

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FP2 (MEI) Calculus 2: Integration using the inverse trigonometric functions

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  1. FP2 (MEI)Calculus 2: Integration using the inverse trigonometric functions Let Maths take you Further…

  2. Integration using the inverse trigonometric functions Before you start… • You need to be familiar with the laws of indices (Core 1 chapter 5) and logarithms (Core 2 chapter 11). • You need to be confident with all the techniques of differentiation and integration in C2 – C4, in particular differentiation using the chain rule, differentiation of trigonometric functions and implicit differentiation (C3 chapter 4), integration by substitution and integration of trigonometric functions (C3 chapter 5) and integration using partial fractions (C4 chapter 10). • You must also be confident with all the work on Trigonometry covered so far, (C2 chapter 10 and C4 chapter 8). • When you have finished…You should: • Recognise integrals of functions of the form and be able to integrate associated functions by using trigonometrical substitutions (pages 11 – 14).

  3. arcsinx arccosx arctan x

  4. Summary of results (these are given in the exam formula book) Now that we have these results we can use the chain rule to differentiate composite functions that include inverse trigonometric functions (this was done in the previous tutorial).

  5. More functions that we can now integrate!!

  6. This result is in the exam formula book Some standard results…. Consider…for example…

  7. Let

  8. This result is in the exam formula book

  9. Three possible methods: Algebraic manipulation Substitution Trigonometric substitution

  10. Algebraic manipulation

  11. Substitution

  12. Trigonometric substitution

  13. Three possible methods: Algebraic manipulation Substitution Trigonometric substitution

  14. Harder integrations

  15. Integration using the inverse trigonometric functions Now you have finished… • Recognise integrals of functions of the form and be able to integrate associated functions by using trigonometrical substitutions (see further examples on pages 11 – 14).

  16. Independent study: • Using the MEI online resources complete the study plan for Calculus 2: Integration using the inverse trigonometric functions • Do the online multiple choice test for this and submit your answers online.

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