Calculus 2
WKST- U-Substitution
Name:____________________________________
Date:_____________________________________
Evaluate the following integrals exactly using the substitution method. In each problem you need to find (i) ,
(ii)
, (iii) integral in terms of , (iv) limits of integration in terms of u (for the definite integrals), and then
(v) evaluate the integral. Use proper notation.
1.
du
=
dθ
€
dθ =
____
2.
du
=
dx
€
3.
dx =
____
, where a >0
du
=
dx
€
dx =
4. If
, find
exactly where c is a constant.
u=
€
du
=
dx
dx =
du
=
dx
dx =
€
5. If
, find
in terms of k.
€
6. If
, find
____
exactly.
du
=
dx
€
____
dx =