nitraiddQ

2021-08-20

Evaluate Definite Integral Using Integral Properties:
If ${\int }_{1}^{7}f\left(x\right)dx=2.5$ and ${\int }_{1}^{7}g\left(x\right)dx=4$, find ${\int }_{1}^{7}\left[4f\left(x\right)-2g\left(x\right)\right]dx$.

hosentak

Step 1
${\int }_{1}^{7}\left[4f\left(x\right)-2g\left(x\right)\right]dx={\int }_{1}^{7}4f\left(x\right)dx-{\int }_{1}^{7}2g\left(x\right)dx$
$=4{\int }_{1}^{7}f\left(x\right)dx-2{\int }_{1}^{7}g\left(x\right)dx$
$=4\left(2.5\right)-2\left(4\right)$
$=10-8$
$=2$

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