MATH 1132Q Worksheet 1 - Math 1132 Worksheet 1 Due 1st...

Math 1132 Worksheet 1 Due : 1st discussion section in the week of Jan. 27th
Integration by Substitution (Review)
Part 1 : Compute the indefinite integral in three steps: (1) specify the substitution u =?
and du =?, (2) rewrite the integral completely in terms of the new variable u , (3) compute
the new integral and express the final answer in terms of the original variable.
Example . Evaluate
Z
x
x
2
+ 1
dx .
Solution .

3. Evaluate
Z
1 + x
1 - x
dx .
4. Evaluate
Z
1
x ln x
dx .
5. Evaluate
Z
sin
3
x dx . (Hint: sin
2
x = 1 - cos
2
x .)

Part 2 : Express the definite integral in x as a new definite integral in the new variable