# Suppose int_5^6 f(x)dx=6 and int_5^6 g(x)dx=2.Evaluate int_5^6 (4f(x)-2g(x))dx.

Suppose ${\int }_{5}^{6}f\left(x\right)dx=6\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}{\int }_{5}^{6}g\left(x\right)dx=2$.
Evaluate ${\int }_{5}^{6}\left(4f\left(x\right)-2g\left(x\right)\right)dx$.
Remember to include a "+C" if appropriate.

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hosentak

Step 1
Need to use the basic properties of definite integrals to find the sum of these integrals.
${\int }_{5}^{6}\left(4f\left(x\right)-2g\left(x\right)\right)dx={\int }_{5}^{6}4f\left(x\right)dx-{\int }_{5}^{6}2g\left(x\right)dx$
$4{\int }_{5}^{6}f\left(x\right)dx-2{\int }_{5}^{6}g\left(x\right)dx$
=4(6)-2(2)
=24-4
=20

Jeffrey Jordon