Review for Test 2

61)
8
∑
k = 1
k3
62)
6
∑
k = 1
k2 - 4
63)
21
∑
k = 3
5
Express the sum in sigma notation.
64) 5 + 6 + 7 + 8 + 9 + 10
65) 1 3 + 1 9 + 1 27 + 1 81
Write the sum without sigma notation and evaluate it.
3
k + 4
66) ∑
k
k = 1
67)
3
∑
k = 1
(-1)k (k - 5)2
68)
4
∑
k = 1
k2
2
Solve the initial value problem.
69) dy
dx = 2x -3/4, y(1) = 10
70) ds
dt = cos t - sin t, s π 2 = 5
Evaluate the integral.
71)
∫
3
11
x dx
Use a definite integral to find an expression that represents the area of the region between the given curve and the x -axis
on the interval [0, b].
72) y = 21x2