In the secondcolumnare listedthe mostcommonsubstitutions.Theycomefrom the referenceright triangles,
as shownin the figurebelow. We wantany of the substitutionswe use in the integrationto be reversibleso
we can changebackto the originalvariableafterward.The right trianglesin the figurebelowwill help us
reverseour substitutions.
Description:3 triangles.
Example1:
Evaluate
Solution:
Our goal first is to eliminatethe radical.To do so, look up the tableaboveand makethe substitution
so that
Our integralbecomes
Up to this stage,we are doneintegrating.To completethe solutionhowever, we needto express in
termsof Lookingat the figureof trianglesabove,we can see that the secondtrianglerepresentsour
case,with So and , thus