5.5 The Substitution Rule by SGLee - HSKim- SWSun
1-3.Evaluate the given indefinite integral using an appropriate substitution.
1. 
,
.
Calculus-Sec-5-5-Solution
5.5 The Substitution Rule by SGLee - HSKim- SWSun
1-3.Evaluate the given indefinite integral using an appropriate substitution.
1.
,
.
2. 
,
3. 
,
.
5. 
.
6. 
.
7. 
.
8. 
,
.
9. 
.
10. 
.
11-23. Evaluate the definite integral, if it exists.
11. 
. (Because 
is odd function)
12. 
.
13. 
.
14. 
.
15. 
4.
16. 
. (First of all we substitute 
.)
.
17. 
,
18. 
Since
,
first we have
Then,
(Because
is even function.)
Hence
19. 
because 
is odd function.
20. 
.
22. 
.
23. 
because 
is odd function.
24-25. Find the exact area.
24. 
, 
.
25. 
, 
4
26. Let 
be a function symmetrical with respect to 
.
Show 
, when 
.
Since 
.
Hence 
.
because 
is a function symmetrical with respect to 
.
4. 
then 
.
.
21. 
