MATH 101 HOMEWORK 5
Due on Wednesday Oct. 20, 2004.
For full credit, show all work. Calculators are not allowed.
1. (4 marks) Find the area of the finite planar region which lies inside the circle x2 +y 2 = 4
and outside of the circle x2 − 6x + y 2 = 0.
2. (12 marks) Evaluate the integrals:
Z
x2
dx,
(a)
(x2 + 4)3
Z
dx
(b)
.
2
x(x − 1)(x2 − 4)
Z
4x(x + 1)
(c)
dx.
(x − 2)2 (x2 + 1)
Z
3. (4 marks) Decide whether the integral
answer.
0
2
2 − sin x
dx is convergent. Justify your
2−x
This homework covers Sections 6.2–6.4 of the textbook. Additional recommended exercises:
Section 6.2, 1–28, 40–46; Section 6.3: 1–26 (fairly straightforward), 27–34 (combine partial
fractions with other techniques, e.g. substitution); Section 6.5: 1–41.
1