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2) Suppose \int_{-2}^{5} f(x)dx = 18, \int_{-2}^{5} g(x)dx = 5, \int_{-2}^{5} h(x)dx = -11, and \int_{5}^{8} f(x)dx = 0, find a) \int_{-2}^{5} [f(x) + g(x)] dx 18 + 5 = 23 b) \int_{-2}^{5} [f(x) - g(x) - h(x)] dx 18 - 5 + 11 = 24 c) \int_{-2}^{5} 4g(x) dx 4(5) = 20 d) \int_{-2}^{5} [g(x) + 2] dx 5 + 2 = 7 e) \int_{-2}^{5} [f(x) - 6] dx 18 - 6 = 12 f) \int_{-2}^{5} \frac{1}{2}[h(x) + 5] dx \frac{1}{2}(-11) + 5 = -\frac{11}{2} + 5 = \frac{-11 + 10}{2} = -\frac{1}{2} g) \int_{0}^{7} h(x - 2) dx h) \int_{-4}^{3} g(x + 2) dx i) \int_{5}^{8} f(x) dx j) \int_{8}^{7} [1 - f(x)] dx k) \int_{1}^{8} [f(x - 3) + 3] dx l) \int_{2}^{9} [2f(x - 4) - 6] dx 3) Evaluate the following by making a sketch of the function. a) \int_{-3}^{3} (x + 2)dx b) \int_{-3}^{3} |x + 2|dx c) \int_{-3}^{3} ||x| + 2|dx d) \int_{-3}^{3} |2 - |x||dx

          2) Suppose \int_{-2}^{5} f(x)dx = 18, \int_{-2}^{5} g(x)dx = 5, \int_{-2}^{5} h(x)dx = -11, and \int_{5}^{8} f(x)dx = 0, find
a) \int_{-2}^{5} [f(x) + g(x)] dx
18 + 5 = 23
b) \int_{-2}^{5} [f(x) - g(x) - h(x)] dx
18 - 5 + 11 = 24
c) \int_{-2}^{5} 4g(x) dx
4(5) = 20
d) \int_{-2}^{5} [g(x) + 2] dx
5 + 2 = 7
e) \int_{-2}^{5} [f(x) - 6] dx
18 - 6 = 12
f) \int_{-2}^{5} \frac{1}{2}[h(x) + 5] dx
\frac{1}{2}(-11) + 5
= -\frac{11}{2} + 5 = \frac{-11 + 10}{2} = -\frac{1}{2}
g) \int_{0}^{7} h(x - 2) dx
h) \int_{-4}^{3} g(x + 2) dx
i) \int_{5}^{8} f(x) dx
j) \int_{8}^{7} [1 - f(x)] dx
k) \int_{1}^{8} [f(x - 3) + 3] dx
l) \int_{2}^{9} [2f(x - 4) - 6] dx
3) Evaluate the following by making a sketch of the function.
a) \int_{-3}^{3} (x + 2)dx
b) \int_{-3}^{3} |x + 2|dx
c) \int_{-3}^{3} ||x| + 2|dx
d) \int_{-3}^{3} |2 - |x||dx

2) Suppose ∫-2^5 f(x)dx = 18, ∫-2^5 g(x)dx = 5, ∫-2^5 h(x)dx = -11, and ∫5^8 f(x)dx = 0, find
a) ∫-2^5 [f(x) + g(x)] dx
18 + 5 = 23
b) ∫-2^5 [f(x) - g(x) - h(x)] dx
18 - 5 + 11 = 24
c) ∫-2^5 4g(x) dx
4(5) = 20
d) ∫-2^5 [g(x) + 2] dx
5 + 2 = 7
e) ∫-2^5 [f(x) - 6] dx
18 - 6 = 12
f) ∫-2^5 (1)/(2)[h(x) + 5] dx
(1)/(2)(-11) + 5
= -(11)/(2) + 5 = (-11 + 10)/(2) = -(1)/(2)
g) ∫0^7 h(x - 2) dx
h) ∫-4^3 g(x + 2) dx
i) ∫5^8 f(x) dx
j) ∫8^7 [1 - f(x)] dx
k) ∫1^8 [f(x - 3) + 3] dx
l) ∫2^9 [2f(x - 4) - 6] dx
3) Evaluate the following by making a sketch of the function.
a) ∫-3^3 (x + 2)dx
b) ∫-3^3 |x + 2|dx
c) ∫-3^3 ||x| + 2|dx
d) ∫-3^3 |2 - |x||dx

Added by Brian M.

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