CIE A Level Maths: Pure 3复习笔记5.1.5 Harder Substitution

Harder Substitution

What is integration by substitution?

  • Make sure you are familiar with Reverse Chain Rule and Substitution (RCR)
  • In more difficult questions the substitution will be given to you


How do I integrate using a given substitution?

  • The process is very much the same as before but expect the algebra to be trickier

8.2.5-Notes-subst_giv_eg_soln1 8.2.5-Notes-subst_giv_eg_soln2

  • STEP 1: Differentiate the substitution and rearrange
  • STEP 2: Replace all parts of the integral
    • all x terms should be replaced with equivalent u terms, including dx
    • if a definite integral change the limits from x to u too
  • STEP 3: Integrate and either
    • substitute x back in or
    • evaluate the definite integral using the u limits
  • STEP 4: Find c, the constant of integration, if needed

Worked Example