Trigonometric Substitutions
Trig. substitutions are usually used for integrals that involve square roots of quadratic expressions; the trig substitution is used to eliminate the radical sign; the following substitutions are made:
| Â Term involve in the Integral | Â Term involve in the Integral | Trig. Identity |
  |
 u = a sin q |  cos2 q = 1 - sin2 q |
  |
 u = a tan q |  sec2 q = 1 + tan2 q |
  |
 u = a sec q |  tan2 q = sec q -1 |
where a is any real number and u is any variable.
ex.
Substitute: x = sec q
dx = sec q tan q dq
 
Substitute:
u = sin q
du = cos q dq
The solution must be in terms of x:
From the substitution of x = sec q, the diagram of a right triangle gives;
The final solution in terms of x is:
Subject:
Subject X2:
