MATH 101 HOMEWORK 5
Due on Wednesday, October 15
Covers sections 6.2, 6.3, and part of 6.5. For full credit, show all work.
1. (4 marks) Find the area of the finite planar region that lies inside the circle x2 +y 2 = 25
and above the line x + y = 7.
2. (12 marks, 4 for each part) Evaluate the integrals:
Z
√
(a)
x3
dx, for x > 0,
x2 − 1
Z
(b)
(x2
−
Z
(c)
1)(x2
x
dx,
− 4)(x2 − 9)
2
(x −
1)2 (x2
+ 4)
dx.
Z
3. (4 marks) Evaluate the integral
0
π/2
dx
, or show that it diverges.
sin3 x
1