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Activity 4.3.3.
Suppose that the following information is known about the functions \(f\text{,}\) \(g\text{,}\) \(x^2\text{,}\) and \(x^3\text{:}\)
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\(\int_0^2 f(x) \, dx = -3\text{;}\) \(\int_2^5 f(x) \, dx = 2\)
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\(\int_0^2 g(x) \, dx = 4\text{;}\) \(\int_2^5 g(x) \, dx = -1\)
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\(\int_0^2 x^2 \, dx = \frac{8}{3}\text{;}\) \(\int_2^5 x^2 \, dx = \frac{117}{3}\)
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\(\int_0^2 x^3 \, dx = 4\text{;}\) \(\int_2^5 x^3 \, dx = \frac{609}{4}\)
Use the provided information and the rules discussed in the preceding section to evaluate each of the following definite integrals.
(a)
(b)
(c)
\(\int_0^5 (f(x) + g(x))\, dx\)
(d)
\(\int_2^5 (3x^2 - 4x^3) \, dx\)
(e)
\(\int_5^0 (2x^3 - 7g(x)) \, dx\)
