MATH2225: Written Assignment #2
Due: 1 March 2023
1. Find the area of the region inside both of the circles x2 +y 2 = 1 and (x−2)2 +y 2 =
4.
2. Find the area in the first quadrant, above the hyperbola xy = 12 and inside the
circle x2 + y 2 = 25.
3. For each of the following integrals, find its value or show that it diverges.
Z ∞
1
(a)
dx
(2x − 1)2/3
3
Z −1
dx
(b)
2
−∞ x + 1
Z 1
dx
(c)
2/3
−1 (x + 1)
Z ∞
dx
(d)
x ln(x)
e
Z ∞
dx
(e)
x(ln(x))2
e
4. Determine whether each of the following integrals converges or diverges. Justify
your answer.
Z ∞
x2
dx
(a)
x5 + 1
0
Z 1
ex
dx
(b)
−1 x + 1
1