Definite Integrals: Numerically
Given the following information:
(a)
3
∫ f(x) dx = 7
1
 (b)
2
∫ f(x) dx = 3
1
 (c)
3
∫ f(x) dx = 1
5
 (d)
5
∫ g(x) dx = -1
2

Find the following (fill in the blank) and then below, carefully justify each step by citing exactly which property from class (or from the textbook) you are using.

(i)
3
∫ f(x) dx =
2
 (ii)
5
∫ f(x) dx =
3
 (iii)
5
∫ f(x) dx =
2
 (iv)
5
∫ f(t) dt =
2
 (v)
5
∫ 3f(x)-2g(x) dx =
2

Your work, step by step justification, and citation of properties you used (label (i) through (v) below) follows: