Assume that we have functions f(x) and g(x) so that \int_{-1}^{3}f(x)dx=-1, \int_{3}^{5}f(x)dx=4, \int_{-1}^{1}g(x)dx=3, \int_{1}^{5}g(x)dx=2 Determine \int_{-1}^{5}(2f(x)-5g(x))dx.

shadsiei 2021-02-14 Answered
Assume that we have functions f(x) and g(x) so that
13f(x)dx=1,35f(x)dx=4,11g(x)dx=3,15g(x)dx=2
Determine
15(2f(x)5g(x))dx.
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Expert Answer

Demi-Leigh Barrera
Answered 2021-02-15 Author has 97 answers
Step 1
Given:
13f(x)dx=1
35f(x)dx=4
11g(x)dx=3
15g(x)dx=2
To find:
15(2f(x)5g(x))dx
Step 2
Using difference rule, we get:
15(2f(x)5g(x))dx=15(2f(x))dx15(5g(x))dx
the constant can be taken out of the integral, hence we get:
15(2f(x)5g(x))dx=215f(x)dx515g(x)dx
Step 3
splitting the above integrals, we get:
15(2f(x)5g(x))dx=2(13f(x)dx+35f(x)dx)
5(11g(x)dx+15g(x)dx)
plugging in the given values of these integrals, we get:
15(2f(x)5g(x))dx=2(1+4)5(3+2)
Jeffrey Jordon
Answered 2021-11-05 Author has 2070 answers

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